Fall23_lec2_defining_computation-Copy1.ipynb

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   "source": [
    "# CS 121 Lecture 4 : Defining computation"
   ]
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   "execution_count": 96,
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    "%%html\n",
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  {
   "cell_type": "markdown",
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   "source": [
    "# Utilities"
   ]
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   "execution_count": null,
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   "source": [
    "import schemdraw\n",
    "import schemdraw.logic as logic\n",
    "import schemdraw.elements as elm"
   ]
  },
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   "source": [
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'svg'"
   ]
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   "source": [
    "class Bit:\n",
    "    \"\"\"A class representing a logical bit. \n",
    "       Keeps track of operations that are done to it\"\"\"\n",
    " \n",
    "    def __init__(self, program):\n",
    "        self.program = program if isinstance(program,tuple) else (program,)\n",
    "  \n",
    "    def op(self,oper, other = None):\n",
    "        if other is None:\n",
    "            return Bit((oper,self.program))\n",
    "        return Bit((oper,self.program,other.program))\n",
    "        \n",
    "    def __and__(self,other): return self.op(\"∧\", other)\n",
    "    def __or__(self,other): return self.op(\"∨\", other)\n",
    "    def __invert__(self): return self.op(\"¬\")\n",
    "    \n",
    "    def __repr__(self): return f\"Bit({self.program})\" \n",
    "\n",
    "def NAND(a,b):\n",
    "    if isinstance(a,Bit) and isinstance(b,Bit):\n",
    "        return a.op(\"N\",b)\n",
    "    return ~(a&b)"
   ]
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   "source": [
    "def AND(a,b): return a & b\n",
    "\n",
    "def OR(a,b): return a | b\n",
    "\n",
    "def NOT(a): return ~ a"
   ]
  },
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   "source": [
    "a = Bit(\"a\")\n",
    "b = Bit(\"b\")\n",
    "c = a & b\n",
    "print(a)\n",
    "print(b)\n",
    "print(c)"
   ]
  },
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   "source": [
    "def bits(n):\n",
    "    return [Bit(f\"X[{i}]\") for i in range(n)]"
   ]
  },
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   "cell_type": "code",
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   "source": [
    "def p2f(P):\n",
    "  \"\"\"Recursive function to transform a program of a Bit into a formula\"\"\"\n",
    "  if len(P)==1:\n",
    "    return P[0]\n",
    "  if len(P)==2:\n",
    "    return P[0] + p2f(P[1])\n",
    "  if len(P)==3:\n",
    "    return f\"({p2f(P[1])} {P[0]} {p2f(P[2])})\"\n",
    "  return f\"{P[0]}(\"+\",\".join([p2f(P[i]) for i in range(1,len(P))])+\")\"\n",
    "\n"
   ]
  },
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   "cell_type": "code",
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   "source": [
    "counter = 0\n",
    "def AON_(P):\n",
    "    \"\"\"Recursive function to transform a program of a bit into an AON straightline program\"\"\"\n",
    "    def uid():\n",
    "        global counter\n",
    "        counter +=1\n",
    "        return f\"z_{counter}\"\n",
    "    funcs = {\"∧\": \"AND\", \"∨\": \"OR\", \"¬\": \"NOT\", \"N\":\"NAND\" }\n",
    "    if len(P)==1:\n",
    "        return \"\",P[0]\n",
    "    op = funcs[P[0]]  \n",
    "    if len(P)==2:\n",
    "        prog, out_ = AON_(P[1])\n",
    "        out = uid() \n",
    "        return prog+f\"{out} = {op}({out_})\\n\", out\n",
    "    if len(P)==3:\n",
    "        prog1,out1 = AON_(P[1])\n",
    "        prog2,out2 = AON_(P[2])\n",
    "        out = uid()\n",
    "        return prog1+prog2+f\"{out} = {op}({out1},{out2})\\n\", out"
   ]
  },
  {
   "cell_type": "code",
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   "source": [
    "def AON(f):\n",
    "    \"\"\"Take either a function or a bit and return the AON program\"\"\"\n",
    "    global counter\n",
    "    counter = 0\n",
    "    if isinstance(f,Bit):\n",
    "        P = f.program\n",
    "    else:\n",
    "        n = len(signature(f).parameters)\n",
    "        P = f(*bits(n)).program\n",
    "    prog, out = AON_(P)\n",
    "    return prog.replace(out,\"Y[0]\")"
   ]
  },
  {
   "cell_type": "code",
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   "source": [
    "def formula(f):\n",
    "    \"\"\"Take either a function or a bit and return the AON program\"\"\"\n",
    "    if isinstance(f,Bit):\n",
    "        return Math(p2f(f.program))\n",
    "    n = len(signature(f).parameters)\n",
    "    F = p2f(f(*bits(n)).program)\n",
    "    return Math(F)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "source": [
    "def circuit_(P, d : schemdraw.Drawing , dx=0, dy=0, drawn = {}):\n",
    "  \"\"\"Recursive function to draw a circuit. Gets the Bit bit and outputs the circuit used to compute it\"\"\"\n",
    "  if P in drawn:\n",
    "    return drawn[P]\n",
    "  maxx = dx\n",
    "  maxy = dy\n",
    "  outs = []\n",
    "  gates = { \"∧\" : logic.And, \"∨\" : logic.Or, \"¬\": logic.Not, \"N\": logic.Nand } \n",
    "  for c in P[1:]:\n",
    "    dx_ , dy_ , out = circuit_(c,d,dx,dy ,drawn)\n",
    "    outs.append(out)\n",
    "    maxx = max(dx_,maxx)\n",
    "    maxy = max(dy_,maxy)\n",
    "    dy = dy_ + 1\n",
    "  maxx += 2\n",
    "  x,y = maxx,maxy\n",
    "  gate = gates[P[0]] if P[0] in gates else logic.Dot\n",
    "  g = gate(at = (x,y))\n",
    "  if isinstance(g, logic.Dot):\n",
    "    g.label(f\"{P[0]}\")\n",
    "  d += g\n",
    "  for i,out in enumerate(outs):\n",
    "    loc = getattr(g,f\"in{i+1}\") \n",
    "    d += logic.Wire().at(out).to(loc)  \n",
    "  drawn[P] =  x,y, g.out if hasattr(g,\"out\") else (x,y)\n",
    "  return drawn[P]\n",
    "\n",
    "def draw_circ(*Ys):\n",
    "  drawn = {}\n",
    "  dx,dy = 0,0\n",
    "  with schemdraw.Drawing() as d:\n",
    "    d.config(unit=0.5)\n",
    "    for i,y in enumerate(Ys):\n",
    "      label= f\"$Y[{i}]$\"\n",
    "      x,dy_, out = circuit_(y.program,d,dx,dy, drawn)\n",
    "      d += logic.Dot().at(out).label(label)\n",
    "      dy = dy_+2\n"
   ]
  },
  {
   "cell_type": "code",
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   "source": [
    "def circuit(f,n=None):\n",
    "    \"\"\"Take a function or a bit and output circuit\"\"\"\n",
    "    if isinstance(f,Bit):\n",
    "        res = f\n",
    "    else:\n",
    "        if n is None:\n",
    "            n = len(signature(f).parameters)\n",
    "        res = f(*bits(n))\n",
    "    return draw_circ(*res) if isinstance(res,(tuple,list)) else draw_circ(res)"
   ]
  },
  {
   "cell_type": "code",
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   "source": [
    "import re\n",
    "def parse(P):\n",
    "    \"\"\"Take an AON program and split each line into components\"\"\"\n",
    "    result  = []\n",
    "    for line in P.split('\\n'):\n",
    "        split = re.split(\"=|\\(|\\)|,| \",line) \n",
    "        split = [x for x in split if x != \"\"]\n",
    "        if split:\n",
    "            result.append(split)\n",
    "    return result\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "source": [
    "def evalp(tuples,x, debug=True):\n",
    "    \"\"\"Evaluate a parsed program on an input\"\"\"\n",
    "    variables = { f\"X[{i}]\":x[i] for i in range(len(x)) }\n",
    "    for rhs,op,*oper in tuples:\n",
    "        if debug: print(f\"Evaluating {rhs} = {op}({','.join(oper)}):\\t variables = {variables}\")\n",
    "        oper = [variables[o] for o in oper]\n",
    "        variables[rhs] = globals()[op](*oper)\n",
    "    return variables[\"Y[0]\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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     "slide_type": "skip"
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   "source": [
    "def EVAL(P,x, debug=True): \n",
    "    \"\"\"Evaluate an AON-CIRC program on an input x\"\"\"\n",
    "    return evalp(parse(P),x, debug)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
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   "outputs": [],
   "source": [
    "def nparams(P): \n",
    "    \"\"\"Returns number of parameters of an AON-CIRC program P\"\"\"\n",
    "    for i in range(len(P)+1):\n",
    "        if f'X[{i}]' not in P: return i\n",
    "def FUNC(P):\n",
    "    \"\"\"Returns the function that AON-CIRC program P computes\"\"\"\n",
    "    # hack to get signature for small # of params\n",
    "    n = nparams(P)\n",
    "    if n == 1:\n",
    "        def prog(a): return EVAL(P,[a],debug=False)\n",
    "    elif n ==2:\n",
    "        def prog(a,b): return EVAL(P,[a,b],debug=False)\n",
    "    elif n ==3:\n",
    "        def prog(a,b,c): return EVAL(P,[a,b,c],debug=False)\n",
    "    else:\n",
    "        def prog(*x): return EVAL(P,x,debug=False)\n",
    "    return prog"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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     "slide_type": "skip"
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   "source": [
    "import itertools\n",
    "from IPython.display import Markdown, display, Math\n",
    "from inspect import signature\n",
    "\n",
    "def table(f,n=None):\n",
    "  \"\"\"Generate truth table of a function\"\"\"\n",
    "  if n is None:\n",
    "    n = len(signature(f).parameters)\n",
    "  m = max(n+2,len(f.__name__)+4)\n",
    "  res = \"x\".ljust(m) + \" | \" + f\"{f.__name__}(x)\".ljust(m) \n",
    "  res += \"\\n\" + \"-\"*m+\"-|-\"+ \"-\"*m \n",
    "  \n",
    "  for x in itertools.product([0,1],repeat=n):\n",
    "    s = \"\".join([str(c) for c in x])\n",
    "    res += \"\\n\"+ s.ljust(m) + \" | \" + str(f(*x)).ljust(m)\n",
    "  res +=\"\\n\"\n",
    "  return Markdown(res)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "# Lecture"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "__Q:__ Compute $f:\\{0,1\\}^3 \\rightarrow \\{0,1\\}$ s.t.\n",
    "$$f(a,b,c) = \\begin{cases}1 & a+b+c\\geq 2 \\\\ 0 & \\text{otherwise} \\end{cases}$$\n",
    "using $AND$, $OR$, and $NOT$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "__Solution:__    $f(a,b,c) = (a \\wedge b) \\vee (b \\wedge c) \\vee (a \\wedge c)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
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     "slide_type": "slide"
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   "outputs": [],
   "source": [
    "# (a ∧ b) ∨ (b ∧ c) ∨ (a ∧ c)\n",
    "def f(a,b,c): return (a & b) | (b & c) | (a & c)"
   ]
  },
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     "data": {
      "text/markdown": [
       "x     | f(x) \n",
       "------|------\n",
       "000   | 0    \n",
       "001   | 0    \n",
       "010   | 0    \n",
       "011   | 1    \n",
       "100   | 0    \n",
       "101   | 1    \n",
       "110   | 1    \n",
       "111   | 1    \n"
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    "table(f)"
   ]
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     "data": {
      "text/latex": [
       "$\\displaystyle (((X[0] ∧ X[1]) ∨ (X[1] ∧ X[2])) ∨ (X[0] ∧ X[2]))$"
      ],
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   "source": [
    "formula(f)"
   ]
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "circuit(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "z_1 = AND(X[0],X[1])\n",
      "z_2 = AND(X[1],X[2])\n",
      "z_3 = OR(z_1,z_2)\n",
      "z_4 = AND(X[0],X[2])\n",
      "Y[0] = OR(z_3,z_4)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(AON(f))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "__Q:__ Come up with a Boolean circuit that computes $XOR:\\{0,1\\}^2 \\rightarrow \\{0,1\\}$ where $XOR(a,b) = a+b \\mod 2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
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    "def f(a,b):\n",
    "    c = a & b\n",
    "    d = ~c\n",
    "    e = a | b\n",
    "    return d & e\n",
    "circuit(f)"
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   "metadata": {
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    {
     "data": {
      "text/markdown": [
       "x     | f(x) \n",
       "------|------\n",
       "00    | 0    \n",
       "01    | 1    \n",
       "10    | 1    \n",
       "11    | 0    \n"
      ],
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       "<IPython.core.display.Markdown object>"
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     "execution_count": 103,
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   ],
   "source": [
    "table(f)"
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    "__Def I (3.5):__ <font color=\"red\">_Boolean Circuit_</font> $C$ is a DAG where vertices  \n",
    "are <font color=\"blue\">_inputs_</font> labeled   `X[0]` ... `X[n-1]` or <font color=\"blue\">_gates_</font>\n",
    "labeled  $\\wedge$/$\\vee$/$\\neg$.\n",
    "<font color=\"blue\">_Output gates_</font> are additionally labeled with  `Y[0]` ... `Y[m-1]`.<br>\n",
    "For $x\\in \\{0,1\\}^n$,  we denote the output of $C$ on input $x$ by $C(x)$."
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    "__Def II (Section 3.4):__ <font color=\"red\">_AON-CIRC program_</font> $P$ has lines of form\n",
    "`foo = AND(bar,blah)` , `foo = OR(bar,blah)` or `foo = NOT(blah)`. \n",
    "<font color=\"blue\">_Input variables_</font> are named  `X[0]`,...,`X[n-1]`and \n",
    "<font color=\"blue\">_output variables_</font> are named  `Y[0]`..`Y[m-1]`. <br>\n",
    "For $x\\in \\{0,1\\}^n$, we denote the output of $P$ on input $x$ by $P(x)$. "
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    "__Theorem III (3.9):__ For every $f:\\{0,1\\}^n \\rightarrow \\{0,1\\}^m$ and $s\\in \\mathbb{N}$, \n",
    "$f$ is computable by a Boolean circuit of $s$ gates if and only if \n",
    "$f$ is computable by an AON-CIRC program of $s$ lines."
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   "metadata": {
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   "source": [
    "__Q:__ Write an AON-CIRC program that computes $XOR:\\{0,1\\}^2 \\rightarrow \\{0,1\\}$ where $XOR(a,b) = a+b \\mod 2$"
   ]
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   "execution_count": 105,
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   "source": [
    "xorcode = r\"\"\"\n",
    "t1      = AND(X[0],X[1])\n",
    "nott1   = NOT(t1)\n",
    "t2      = OR(X[0],X[1])\n",
    "Y[0]    = AND(nott1,t2)\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "x        | prog(x) \n",
       "---------|---------\n",
       "00       | 0       \n",
       "01       | 1       \n",
       "10       | 1       \n",
       "11       | 0       \n"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xor = FUNC(xorcode)\n",
    "table(xor)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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   "source": [
    "circuit(xor)"
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   "source": [
    "__Q__ Give a circuit/program for computing $XOR_n:\\{0,1\\}^n \\rightarrow \\{0,1\\}$ such that $XOR(x) = \\sum_{i=0}^{n-1} x_i (\\mod 2)$?"
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     "data": {
      "text/markdown": [
       "x        | xor4(x) \n",
       "---------|---------\n",
       "0000     | 0       \n",
       "0001     | 1       \n",
       "0010     | 1       \n",
       "0011     | 0       \n",
       "0100     | 1       \n",
       "0101     | 0       \n",
       "0110     | 0       \n",
       "0111     | 1       \n",
       "1000     | 1       \n",
       "1001     | 0       \n",
       "1010     | 0       \n",
       "1011     | 1       \n",
       "1100     | 0       \n",
       "1101     | 1       \n",
       "1110     | 1       \n",
       "1111     | 0       \n"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def xor3(a,b,c): return xor(a,xor(b,c))\n",
    "table(xor3)\n",
    "def xor4(a,b,c,d): return xor(a,xor3(b,c,d))\n",
    "table(xor4)"
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   "execution_count": 113,
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Dhw6Va1Ha6rK2tuZuP3jwgMdIPk1FRQU7d+6Era0tACAlJQWjR4+WKAhMlNOBAwfw008/cfeDgoLQt29fHiNSTjY2NtztO3fuVPvxAoEAPj4+aNasGb777js4OjrCysoKtra2db6XmOL+pSaEEEIIIaSOKCwsxIEDB2BlZYVBgwYhOjqaW6erq4sFCxYgMTERoaGhYhc3iqxDhw7c7SdPnvAYSdVoamri+PHjMDMzAwBcu3YNK1eu5DkqUlsRERGYNm0ad3/Lli34/vvveYxIeTVq1Ih7fyQkJFTrsSKRCOPGjcP69evx4cMHsXXXr1/HN998g1u3bkktVkVDiRVCCCGEEEJkJCMjAytXrkTz5s0xefJkPH78mFtnYWEBPz8/vHr1Chs3buQuaJRF+doVij4UqIyxsTEOHz4MNTU1AMDatWtx8eJFnqMiNXX79m2MGjUKQqEQQOmUwd7e3jxHpdxatGgBAHj79i03m1ZVnD17FkePHq10fX5+PqZPn466OimxOt8BEEIIIYQQUtf8888/2LZtG4KDg1FUVCS2ztbWFt7e3hg+fDh3ga+MjIyMuNtv377lMZLq6dmzJ9atW4eFCxeCMQYXFxfcu3evxoWBs7Oz4e/vj5ycHLRo0QLNmzdHixYtYGZmBm1tbSlHT8o8e/YMDg4OyM/PBwCMGjUKvr6+UFFR4Tky5WZgYMDdzsrKqvL7Yu/evZ/c5u7du4iJiUG3bt1qHJ+iosQKIYQQQgghUsAYw6VLl7B161ZERkaKrVNVVYWzszO8vb3x1Vdf8RShdGlqanK3y+rEKIv58+fjwoUL+P3335Geno42bdqgUaNGNdpXdnY2cnJyKlxnYmKC5s2bc8mW//7W09OjREANZGRkYODAgcjIyAAA9OnTB8HBwQpdk0hZ1KtXj7ttbW1d5eRvVYtB//PPP5RYIYQQQgghhIgrLi7GoUOH4Ovri/v374uta9iwIaZMmYKZM2eiZcuW/AQoB8rWvf/t27dis5Xk5ORUmhypjbS0NKSlpVVaW6JBgwYfTbw0bdoU6up0yVZeXl4ehgwZwtUAad++PU6dOkW9g6Sk/HtZFjNnlU/I1iX0LiWEEEIIIaQGMjMzsXfvXuzcuVOixkjz5s0xe/ZsTJo0Cbq6ujxFKFvZ2dncbWU6RpFIBDc3N+6iUUdHB40bN67VPgUCAdTV1TFw4EDo6+sjKSkJL1++RFJSElJTUytNPOXm5uLx48ditXfKU1NTQ7NmzSpMvJTdbtCgQa1iVyYCgQDff/89l6hq2rQpIiMjoaenx3NkdUf597WpqWmVewG9f/8eeXl5H91GQ0NDbErnuoQSK4QQQgghhFRDfHw8tm/fjoCAABQUFIit6969O+bNm4cRI0bU+Z4Gb9684W7r6+vzGEn1rF69GlFRUQBKi9nGxcXB2NhYZu0VFxfj1atXYsmW//6urEioUChEUlISkpKS8Oeff1a4jZ6eXoW9Xcp+GxkZ1YkhMowxeHl54ezZswBKZ7CJjIxE8+bNeY6sbilLOKqpqSE5ObnKQ4GePn2Kjh07fnRYoIuLi1htprqkbv+1J4QQQgghRAoYY7h69Sp8fX0RHh4u1gNBRUUFTk5O8Pb2Rs+ePT+bmhnPnj3jbn/55Zc8RlJ14eHhWLFiBYDSujehoaEyTaoApUMfLCwsYGFhUeF6xhgyMjI+mnj5WHHgrKwsZGVl4d69exWu19LSgrm5eaWJF2Upsrt27Vrs27cPQGnPh5MnT6JTp048R1W3MMaQmJgIoLTXXXWKa7du3RphYWEYN24cSkpKJNb37t0bP//8s9RiVTSUWCGEEEIIIaQSJSUlOHr0KHx9fREbGyu2TkdHBxMnTsTs2bOVJrEgTQ8ePOBuW1pa8hhJ1Tx9+hSurq7c/XXr1mHAgAE8RlRKRUUFRkZGMDIyQteuXSvcJi8vD8nJyVyi5b/Jl1evXkEgEFT42KKiIiQkJHA1SSqi6EV2AwICsGzZMu5+YGBgnR1SwqekpCR8+PABANC2bdtqP97Z2Rlt27bFzz//jPDwcBQUFMDS0hJTp07F+PHjoaWlJe2QFQYlVgghhBBCCPmP9+/fw9/fH35+fnj16pXYumbNmmHWrFmYMmXKZ13b4e+//wYAqKuro3PnzjxH83Hv37+Ho6MjVz/C2dkZCxYs4DmqqtPR0UHbtm0rvdgVCoVITU2ttNfLy5cvP1qcV5GL7EZFRWHKlCnc/U2bNmHcuHEyaetzd/36de62jY1NjfZhZWWFvXv3Vmn65bqEEiuEEEIIIYT8n+fPn2PHjh04cOCARCHGLl26YN68eRg9ejQ0NDR4ilAxvH79Gv/88w+A0ilZy0/RqmiKi4sxYsQILt4OHTogICCgTg3ZUlNTg5mZGczMzNCzZ88Kt3n//v1HhxspYpHd2NhYODs7QygUAgBmzpyJ+fPnV3s/pGouXLjA3bazs+MvECVEiRVCCCGEEPJZY4zhxo0b8PX1xcmTJyESicTWDx06FPPmzUOfPn3q1MV4bZQVEAWAQYMG8RjJxzHGMGnSJFy+fBkAYGhoiFOnTn1WM+mUady4MRo3blxpXRJFK7L7/PlzDB48mEtwjhw5Etu2baP3oIyUlJTgzJkzAID69etXmqAjFaPECiGEEEII+SwJBAKcOHECvr6+uHnzpti6evXqwd3dHXPmzEHr1q15ilBxHTx4kLs9ZMgQHiP5uKVLlyI0NBQAoK2tjfDwcLRq1YrnqBSTIhXZNTY2xvnz5/Hu3TsApcNS9u/fX61iqqR6zp07xz3fQ4YMUeheaIqIEiuEEEIIIeSzkp2djQMHDmDHjh14+fKl2DoTExP88MMPmDZtGgwNDXmKULE9e/YMf/zxBwCgTZs2Na7FIGvr16/HunXrAJQWiD148CC+/vprnqNSXnwW2Y2NjYWenp7CF9lVZrt27eJuu7u78xeIkqLECiGEEEII+SwkJSXBz88P/v7+XBHTMh07dsS8efPw/fffK+3MFSKRCCoqKjK/sPT19eVue3h4KOSFrK+vL3x8fLj7fn5+cHJy4jGiz4OiF9k1NzdXyNcr327duoWLFy8CACwsLGBvb89zRMpHhVVWoYgQQgghhJA64Pbt29i6dSuOHTvGFcEsM2jQIHh7e6N///5KfcF16dIlDBkyBKqqqmjcuLHM2hGJREhNTQVQOrQmJSUF+vr6MmuvJvz8/DB79mzu/saNG5VqBqDPFWMMM2bMwJ49ewCUDsebPXs2V7+lKkV2P0VHR6fG7w+BQIA3b94AAHr37o2rV6/WaD+KhjGGvn37cr3Q9u7di6lTp/IclfKhHiuEEEIIIaTOEQqFOHPmDHx9fSWKaWppaWH8+PGYM2cOOnTowFOE0rV161YUFBQAgMRsRrKip6enUEkVxhhWrFiBVatWcctWrVpFSRUlsX79ei6poq6ujjNnzmDAgAES29WmyG5eXp5U3h+VzY6kjA4ePMglVVq1akXDgGqIEiuEEEIIIaTOyM3NRWBgILZv345nz56JrWvSpAm8vLzg6ekJIyMjniKUPsYYYmJiAACqqqowMTGRSe+b8t/Yq6ioYOXKlVJvo6aEQiG8vLywd+9ebtny5cuxdOlSHqMiVRUUFIQlS5Zw9wMCAipMqgA1L7IbExODxMTEGr83yr/+27dvX6N9KJqUlBTMmjWLu+/r6wtNTU0eI1JelFghhBBCCCFK79WrV9i5cyf27t2L9+/fi61r164dvL294eLiUidnukhJSUF6ejoAoF+/foiOjpZ6G4wxfPfdd9y+Fy9ejClTpki9nZp4//49XF1dce7cOW7Zjh07xC4YieK6cOECJk+ezN3fsGEDXF1da7y/qhTZrYmEhARYWloCAJo3by61/fKluLgYY8eO5WYCGj16NIYOHcpzVMqLEiuEEEIIIURp3b17F76+vvjtt98kZhsZMGAAvL298d1330FVVZWnCGUvNjaWuy2rGXqOHDnCJVWaN28u1ruAT48fP4ajoyPi4+MBlA4hCQoKwrhx43iOjFTFnTt3MHLkSO696+XlRUO35IAxhunTp+PatWsAAHNzc/zyyy88R6XcKLFCCCGEEEKUikgkQkREBLZu3YorV66IrdPQ0MC4cePg7e2NTp068ROgnMk6sZKcnAxPT0/u/vbt21G/fn2pt1MdjDEEBwfjhx9+QG5uLgDAwMAAhw8fRv/+/XmNjVRNYmIiBg8ezJ0/Jycn7NixQ6mLSCsDxhjmzp2LgIAAAKVFqI8ePapQ9ZKUESVWCCGEEEKIUsjPz0dwcDC2bduGp0+fiq3T19eHp6cnvLy8YGpqylOE/CifWJHm0AegtHbJ+PHjkZWVBQBwdnaGo6OjVNuorvT0dEybNg2nTp3ilv3vf//DyZMn0bJlS97iIlWXmZmJQYMGcTVLbG1tERYWBjU1NZ4jq9tKSkowbdo0LqmioqKC4OBgfPXVVzxHpvwosUIIIYQQQhRaWloadu3ahV9++QWZmZli6ywtLTF37ly4ubnx3ouCD+UL1+rp6Uk9sbBmzRpuxhBzc3Ps27ePtx4FQqEQAQEB8PHxQUZGBrfczc0Nu3fv/izPvzIqKCjA0KFD8eTJEwBAmzZtcPr06TpZ/0iRpKWlYcyYMdw00SoqKjhw4ABGjRrFc2R1AyVWCCGEEEKIQnrw4AG2bduGsLAwFBcXi62zs7ODt7c3HBwc6nT9lE8pX7jWxsZGqkmPo0ePYsWKFQBKZxsKCwuDnp6e1PZfVYwxXLp0CfPmzUNcXBy33NDQEPv27YOTk5PcYyI1IxQKMW7cONy4cQMAYGJigqioKBgYGPAcWd3FGMPx48fh6emJt2/fAiidWSk0NJSSKlJEiRVCCCGEEKIwGGM4f/48fH19JWa3UVdXx5gxYzB37lyZFWlVNrKqrxITEwM3Nzfu/rp169C7d2+p7b8qBAIBzp49i40bN+Lvv/8WWzd69Gj4+fnB2NhYrjGRmmOMYdasWdwQrgYNGiAyMpKGb8nQ3bt3sWjRIly4cIFb1rRpUxw/fhxff/01j5HVPZRYIYQQQgghvCssLERYWBh8fX3x+PFjsXW6urqYNm0aZs6cCTMzM54iVEyySKy8ePECw4YNQ0FBAYDSoTbymqlFJBLh9u3bOHnyJIKDg5Gamiq23traGtu3b5d7kofU3saNG7F7924ApUnSEydO4H//+x+/QdVBQqEQly5dgp+fH86ePSu2ztHREfv27UOTJk14iq7uosQKIYQQQgjhTUZGBnbv3o1du3aJ1c0AAAsLC8yZMwceHh5o0KABTxEqNmkXrk1NTYW1tTVXrNbS0hIrV65EWloaGGMSPwAqXF7VdQUFBXjx4gWePn2K27dv4/r169zQpvKsrKywaNEijB079rMe+qWsQkJCsHjxYu7+r7/+im+//ZbHiOqWzMxM3LhxA1FRUTh16hRSUlLE1jdv3hzbtm2Dk5MTzbokIyqs7C8bIYQQQmQmKysLQqFQ5u3o6OhQAUCiFP755x9s27YNQUFBEvVTTE1N0blzZ3zxxRdyu4jW0NCAjo4OjI2N0bJlS7Rv316u7dcEYwwmJiZIT0+Hnp4eMjMza3XRxBhTqONVVVWFlZUVHB0d4erqii+//FKh4vuYlJQUdOvWDR4eHli7di3f4fAqOjoagwcPhkAgAFA6rKx8kkVZJCQkwNLSEkBpwtHe3l7uMXz48AGhoaFo06YNunTpgtTUVCQkJEgkUsqYm5tj/vz5mDZtGrS0tOQc7eeFEiuEEEKIDDHGMHToUJw7d05ubWpra8PExARt27ZFhw4dYGtri969e8PQ0FBuMRBSkbIipFu3bkVkZCTf4XySvr4+bG1tMXjwYDg6OsLExITvkMS8evUK5ubmAIABAwZI1KSprvj4eLRu3VoaocmEop+P8sonuMaOHYtff/0V2traPEbEj3v37qFPnz7IyckBAHh6emLXrl1K2Wvi2bNnaNWqFd9hfJKGhga+++47uLu7Y9iwYdDQ0OA7pM8CJVYIIYQQGcrNzYWenh73TR2fbG1t4ezsjLFjx1LBRyJXxcXFOHToEHx9fXH//n2+w6kRNTU1DBw4EDNnzoS9vb1CXBiePn0ajo6OAICFCxdiw4YNtdpf+W/kFZ0ino/yNDU1UVJSwt23trbGsWPH8MUXX/AYlXy9ePECPXr0QFpaGoDS+h7Hjh2Dmpoaz5HVjEgkgo2NDe7du8d3KGIMDAzQrl07dO/eHb169cKAAQPQsGFDvsP67FBihRBCCJGxRYsWYePGjdz9L774Au3bt5d6O4wx5OXlITMzE0lJScjOzq5wO01NTYwZMwYzZ85Et27dpB4HIWUyMzOxd+9e7Ny5U6IIafPmzeHi4oL169cDAAYOHIjVq1fzESYYYygpKUFOTg7S0tKQkJCAuLg43Lhxg5uetLwuXbpg3bp1GDhwIA/R/n/Lly/nnrMjR47UeurU8okVOh+14+rqirCwMLFlenp6CAkJgYODA09Ryc+7d+9ga2uLf//9FwDQo0cP/P7770o/VFUoFOL+/ftyGdpbmYyMDJiamqJhw4YwNjam+lOKghFCCCFEpoRCIXNzc2MAGADWoEEDdu/ePZm2KRKJWEpKCjtz5gybP38+a9++Pdd++R97e3t29+5dmcZCPj9Pnz5lM2bMYPXq1ZN4zXXv3p0dPnyYlZSUsPj4eG65i4sL32FLEAqFLCYmhvn4+DBzc3OJYxk6dCh7+fIlb/ENHjyYi+X58+e13h+dD+lxcXGp8G8uAObj48MEAgHfIcpMfn4+s7W15Y63devW7O3bt3yHRYhMUWKFEEIIkYOSkhI2bNgw7oPmF198IfcPmo8fP2YLFixg+vr6Yh/yVVRUmKurK3v9+rVc4yF1i0gkYleuXGHDhg1jKioqEq+xESNGsD///JOJRCLuMYp+IV+eQCBgx48fZ9bW1mLH1qhRIxYWFib3eEQiETMyMmIAmJ6entjzWlN0PqSnfGIlJiaGOTk5icXZr18/lpaWxneYUicQCNiIESO44zQ2NpZK0o8QRaccZbUJIYQQJaeuro7ffvuNG3qTmJiIsWPHyrX2Srt27bBx40YkJyfD398fLVq0AFDa7T40NBTt27dHUFAQNxUqIVVRUlKCgwcPolu3brCzs8OZM2e415COjg5mzpyJ+Ph4HD9+HLa2tgpXC6Oq1NTUMGLECNy+fRsHDx5E06ZNAQDZ2dlwcXHB7Nmz5fp+TklJ4aYltrGxUdrntaYU7Xx8jK6uLo4fP44tW7Zw9UUuXboEa2tr/PnnnzxHJz2MMcyZMwcnTpwAADRo0AARERGfVV0Z8vmixAohhBAiJ/Xq1cOJEydgZGQEoHQKyuXLl8s9jvr162Py5Ml48uQJfH19oa+vDwB4//493N3dMXjwYK7YICGVef/+PTZv3gwLCwu4uLggNjaWW9esWTMuiefn54cvv/ySx0ilS1VVFWPHjsXjx48xfvx4brmfnx+cnZ1RWFgolzjKP982NjZyaVMRKcr5+BQVFRXMmzcPly5d4mYzev36Nezs7LBt27Y6kdDevHkzdu7cCaD0y4Rjx47B2tqa56gIkQ9KrBBCCCFyZGZmhqNHj0JdXR0AsGHDBly/fp2XWLS0tDB37lw8ffoUrq6u3PKoqChYW1vj2rVrvMRFFNvz588xe/ZsmJmZYcGCBXj16hW3rkuXLggNDUViYiIWLFgAPT09HiOVLV1dXQQHB2Pfvn3cdKanT5/GyJEjUVRUJPP2KbEiju/zUVV9+vTB3bt3YWdnB6C0GKq3tzdGjRpVacFxZRAWFoaFCxdy9/fv34/vvvuOx4gIkS9KrBBCCCFy1qdPH6xZswZAaddpNzc35OXl8RaPgYEBQkJCEB4eDlNTUwBAamoq+vbti61bt9aJb1JJ7TDGcP36dTg7O8PS0hJ+fn5ir9mhQ4fiypUriI2NhYuLC3dh+zmYMmUKIiIioKOjAwCIiIiAh4eHzN835RMrXbt2lWlbyoSv81EdJiYmiI6OxqJFi7hlx48fR9euXfHgwQMeI6uZ33//HR4eHtz9NWvWwM3NjceICJE/SqwQQgghPJg/fz569OgBoHSKUx8fH54jAoYMGYJ79+6hX79+AEq/SZ0/fz6mTZumMLUKiHwJBAIcOXIEPXr0gK2tLY4fPw6RSASgdGibp6cnnjx5gjNnzuCbb7757Op8lBkwYAAiIiK4qWQPHTqEdevWyaw9xhhiYmIAlE7h27JlS5m1pYzkfT5qQl1dHevXr8fp06ehq6sLAIiPj8dXX32F4OBgnqOruri4ODg5OaGkpAQAMG3aNIX4f0aIvFFihRBCCOGBmpoagoKCuA/+O3fuxOPHj3mOCjAyMsKFCxewZMkSbpm/vz8cHR157VVD5Cs7Oxvbtm1Dq1atMGbMGNy8eZNbZ2JigjVr1iApKQm7d+9G69ateYxUcfTp0weHDh3ikkvLly/HH3/8IZO2PvfCtVUhz/NRG8OGDcOdO3fQpUsXAEBBQQHc3Nwwbdo0hakPU5mXL19i0KBByMnJAVB6LDt37qTXI/ksUWKFEEII+QjGmMy6kFtaWmLp0qUAAJFIhB9//FEm7VSXmpoa1qxZg4MHD3JDOs6dO4d+/fohKyuL5+iILCUlJWH+/PkwNzeHt7c3Xr58ya3r2LEjAgMD8eLFCyxZsgSGhobUk+k/hg8fjpUrVwIofU9PnDhRJglJqq9SNfI6H7VlYWGB69evY/Lkydyyffv2wdbWFomJiTxGVrl3795h0KBBSE1NBQB8/fXXOHToEFc/jJDPDb3yCSGEkAqkpKRg1apVCAoKgrq6OnR1dWXyLRxjDGpqahAKhYiIiMDy5cuxatUqqbdTE2PHjoWJiQkcHR2RnZ2NW7du4dtvv0V0dHSdLkr6Obp9+za2bt2KY8eOQSgUiq0bNGgQvL290b9/f7H3QEhICKZPnw5VVVU0atSoRu+P8omZpKSkmh+AAvHx8UF0dDSuXbuG58+fY+3atVIfhlI+sdKpUyccO3YMgYGBuHDhAjQ1NWv894rOB3+0tbXh7+8PW1tbeHp6orCwEHfu3IGNjQ1CQkLg4ODAd4icwsJCODo64p9//gFQ+iVBeHg46tevz3NkhPBHhSlSJSdCCCGEZ+/evcOGDRvw888/89INu1GjRvjw4YPc2/2YBw8eYMCAAWJDDyi5ovyEQiHOnDkDX19f/Pnnn2LrtLS0MH78eMyZMwcdOnSQeOy5c+cwfPhwiSRMbRgYGODt27dS2x+f4uPjYWVlheLiYmhpaeHp06do3ry51Pbv4OCAiIgIAKV/M2Qxmwydj9pxdXVFWFgY136rVq2q/Ni4uDg4OzsjISGBW+bj44NVq1ZBTU1N6rFWh1AoxPfff49jx44BKB0+euPGDVhYWPAaFyF8ox4rhBBCCIC8vDzs2LEDmzZtEkts1KtXD7q6ujL/MJuWlgahUIjs7Gw8fPgQVlZWMm2vOjp27IjLly+jb9++SE9PR2xsLOzt7XH58mU0aNCA7/BINeXm5iIwMBDbt2/Hs2fPxNY1adIEXl5e8PT0hJGRUYWPv3XrFkaPHs0lVfT19blaQdUlEAjw5s0bAED79u1rtA9FZGlpidmzZ2Pz5s0oKirCpk2bsHPnzlrvNzU1FSEhITh//jy3rHxSxcDAAJqamlBVrdlofzofiqFz586IiYmBh4cHTp48CQBYt24d/v77bxw8eBDGxsa8xMUYg7e3N5dU0dHRQUREBCVVCAEARgghhHzGioqK2K5du5ixsTEDwP1oaWmxefPmsYyMDLnE4efnx7U9adIkubRZXY8ePWJGRkZcnPb29qyoqIjvsEgVJScns4ULF7LGjRuLvdYBsHbt2jF/f3+Wn5//0X3Ex8czQ0ND7nFjxoxhQqGwxjHFx8dz+3JxcanxfhTR27dvmY6ODgPAtLW1WWZmZo32U1hYyI4ePcocHByYmpqaxLmrV68ec3V1ZRcvXqzVuWCMzoc0ubi4cM9lfHx8jfYhEonYli1bxM5706ZN2bVr16QcbdVs3ryZi0NNTY1FRETwEgchioiK1xJCCPksiUQiHDx4EO3atYOXlxf3La2qqiomTZqE+Ph4bNmyBYaGhnKJx93dHY0aNQIAHD58GAUFBXJptzrat2+PS5cucUOALly4gMmTJ8usuC+Rjrt372L8+PH44osvsHHjRrx//55bVzYt7cOHDzF58uSP9jxJT0/HwIEDueEh33zzDYKCgmrcO6KuMzAwwKRJkwCU1qQICQmp8mMZY7h9+za8vLxgamqKUaNG4dy5cxJDrwYOHIi0tDSEhISgf//+dC4+ojbngy8qKiqYN28eLl++DFNTUwDA69evYWdnh23btsn1b++hQ4fECqz7+/tj0KBBcmufEEVHf30JIYR8VhhjiIyMhLW1NVxcXPD8+XNu3ciRI/Hw4UPs378f5ubmco2rYcOGGDlyJIDSoRqRkZFybb+qOnTogDNnzkBbWxtAaQFTHx8fnqMi/yUSiXD27Fn07dsX1tbWCA0N5QqTamhowM3NDXFxcYiOjsagQYM+eUGel5eHIUOGcEOHOnTogFOnTkFLS0vmx6LMpk6dyt0+dOjQJ7dPTU3F5s2bYWVlhe7du2P37t1iM3GZm5ujV69e3P2JEydyCVnyadU9H4qid+/euHPnDuzs7ACU1jnx9vbGqFGjZFJf578uXboENzc37v6qVavg4eEh83YJUSaUWCGEEPLZuH79Ouzs7DB48GDExcVxy/v164ebN2/i2LFjaNeuHW/xjR49mrt97tw53uL4lF69euHQoUPcxfiGDRu4Io2EX/n5+dizZw/atWuHoUOH4sqVK9w6fX19LFmyBC9fvkRgYCA6depUpX0KBAKMHj0at2/fBgA0a9YMkZGRaNy4sQyOoG7p0KED9zzfvHkTKSkpEtsUFRXh2LFjGDJkCMzNzbFgwQI8fvyYW1+vXj24urri4sWLePHihVgipWvXrrI/iDqkKudDUZmYmCA6OhqLFi3ilh0/fhxdu3bFgwcPqrSP/Px8BAUFYdGiRZg7dy5Wr179ycfev38fTk5OKCkpAQBMmTIFS5curfmBEFJX8TsSiRBCCJG9Bw8esGHDhknUJrCxsWHR0dF8h8fJz89nWlpaDABr2bIl3+F80s8//8w9l9ra2uz27dt8h/TZSk1NZUuXLmUGBgYSr3NLS0u2e/dulpeXV+39ikQiNnnyZG5fjRo1Yvfv35da3HW5pkeZpUuXcscYHBzMGCt9Xm/dusVmzJjB9PT0JM4ZANarVy+2f/9+9uHDB25fIpGIq3Okp6fHRCKRVGP9XM+HLEijxkplTp8+zXR1dcXq7AQFBVW6fW5uLps/f36lr7XevXuz33//XeJxL1++ZE2bNuW2GzJkCCspKZHqsRBSV1BihRBCSJ2VmJjIJkyYwFRUVMQ+RLZu3ZodPXpU6hcl0mBnZ8fF+fr1a77D+SiRSMSmTJnCxdusWTOWmprKd1iflfv37zMPDw+mqakpcbFkZ2fHzpw5U6uCpitXruT2p6mpyS5duiTF6D+PC/lLly5xx+jm5sY2bdrE2rdvX+EFrrm5OVu6dCl7+vRphftKTk7mth0wYIDUY/3czseMGTNk1o4sEyuMMfbs2TPWpUsXsdfP1KlTWUFBgdh27969Y127dq3w9Vb+R01NjQUEBIg9rvzrtHv37iw3N1fqx0FIXUFDgQghhNQ5b968waxZs9C6dWsEBwdzBf6aNWsGf39/PHr0CM7OzlBRUeE5UknW1tbc7ap27+aLiooKdu7cCVtbWwBASkoKRo8ezdXyILLBGENUVBTs7e3RqVMnBAQEoLi4GACgrq4OFxcXxMTE4PLlyxg6dGiNC5oeOHAAP/30E3c/KCgIffv2lcoxfE7KT50eFBT0yaE+q1evhqWlZYX7io2N5W7b2NjILug6rPzzdufOHR4jqR0LCwtcv34dU6ZM4Zbt27cPtra2SExMBFBai8XJyQkxMTEASusrTZgwAefOncNff/2F7du3o02bNty2kyZNwoULF1BYWAhHR0fuddqqVSucPXsWOjo6cj5KQpSHOt8BEEIIIdKSnZ2NLVu2wNfXF3l5edxyPT09+Pj4wMvL66OzniiCDh06cLefPHkCe3t7HqP5NE1NTW6c/6tXr3Dt2jWsXLkSq1ev5ju0OqewsBBhYWHw9fUVuzAHAF1dXUybNg0zZ86EmZlZrduKiIjAtGnTuPtbtmzB999/X+v9fi4YY4iJiUFgYGClRVJ79eoFd3d3jBo1qsoFaCmxUnuNGjWCmZkZXr16hYSEBL7DqRVtbW3s27cPPXv2hKenJwoLC3Hnzh3Y2Nhwsx798ccfAAAjIyNcvHgRHTt25B7fs2dP/PDDD5g9ezZ27doFkUiEJUuW4IsvvsDVq1cBAE2aNEFUVBSaNGki/wMkRIlQYoUQQojSKywsxO7du7Fu3TpkZmZyy+vXr4+5c+di/vz5SlNos/xsRKmpqTxGUnXGxsY4fPgw+vTpA6FQiLVr1+Kbb77BgAED+A6tTsjIyMDu3buxa9cuZGRkiK2zsLDAnDlz4OHhgQYNGkilvdu3b2PUqFHc1L6zZ8+Gt7e3VPZd16WmpiI0NBSBgYESya8yixYtwsSJEyvtlfIx5RMrVLi25lq0aIFXr17h7du3KCws5GY5U1bu7u7o0qULnJ2dkZCQgKysLAwZMgRffvklt82ePXvEkipl1NTU4Ofnhz///BNxcXGIiYnherjUr18f586dE9sPIaRilFghhBCitAQCAYKDg7FixQokJydzy9XV1TFt2jQsXboUJiYmPEZYfUZGRtztt2/f8hhJ9fTs2RPr1q3DwoULwRiDi4sL7t27B1NT0xrtLzs7G/7+/sjJyUGLFi3QvHlztGjRAmZmZkp/EVRV//zzD7Zt24bg4GAUFRWJrbO1tYW3tzeGDx8ONTU1qbX57NkzODg4ID8/HwAwatQo+Pr6KuSwOUVRVFSE8PBwBAYGIioqiktIlalXrx4MDAzw6tUrAMCsWbNq9L5gjOHGjRsASnvhtWzZstaxf64MDAy421lZWTX+O6VIOnfujJiYGHh4eODkyZMAwE2P3qxZMwwbNqzSx6qqqsLLy0tsOmo1NTUcPXoU3bp1k23ghNQRlFghhBCidBhjOHnyJJYsWYJ///2XW66iooJx48Zh5cqVSvsNm6amJne7rG6Gspg/fz4uXLiA33//Henp6WjTpk2Vhzj8V3Z2NnJycipcZ2JigubNm3PJlv/+1tPTU9pEAGMMly5dwtatWxEZGSm2TlVVFc7OzvD29sZXX30l9bYzMjIwcOBArldMnz59EBwcXOMaLXXZf4f6ZGVlSWxTfqjP1KlTcfjwYQCldZRqkgwTCARcO0KhUGlf44qg/JDQmp4PACgoKEBubi4aNGggMcz03bt33O3IyEjMnDmzZsFWg66uLo4fP47169djyZIl3PKGDRt+8hj/97//id3fu3cvBg8eLIswCamTKLFCCCFEqVy+fBmLFi3CrVu3xJY7ODhg7dq16Ny5M0+RSV9Z0V1l8fbtWzx69Ii7n5OTU2lypDbS0tKQlpYm8Roo06BBg48mXpo2bQp1dcX6CFRcXIxDhw7B19cX9+/fF1vXsGFDTJkyBTNnzpRZL4W8vDwMGTKEqznRvn17nDp16rPpHVRVnxrqY25uDjc3N0yYMEFsqE/593JaWlqt48jOzkZkZCQGDRpU6319jqR9PsonUSqyf/9+uSRWAODFixc4fvy42DINDY1PPq6kpIS73b17d0yaNEnqsRFSlynWpwpCCCGkErGxsfDx8cGFCxfEltva2mL9+vXo3bs3T5FJV3Z2NndbV1eXx0iqRyQSwc3NjbtI0dHRqXVdG4FAAHV1dQwcOBD6+vpISkrCy5cvkZSUhNTU1EoTT7m5uXj8+HGlNS7U1NTQrFmzChMvZbelVa/kUzIzM7F3717s3LlToqZO8+bNMXv2bEyaNEmmrwWBQIDvv/+eS1Q1bdoUkZGR0NPTk1mbyqQqQ31GjhwJd3d39O3bt8IePuXf16ampjXuBZSXl4f3798DKB1S9PDhQ2hpadVoX58zaZ2PT/VYKSgoAABMnjy55sFWw7lz5+Dq6sq9Rso8ffoUmZmZYkOg/qts+BAAjB49WlYhElJnUWKFEEKIQnv69CmWLVuGI0eOiC23srLC+vXr4eDgUKe6xL9584a7ra+vz2Mk1bN69WpERUUBKC1mGxcXB2NjY5m1V1xcjFevXoklW/77u7CwsMLHCoVCJCUlISkpCX/++WeF2+jp6VXY26Xst5GRUa2GyMTHx2P79u0ICAjgLr7KdO/eHfPmzcOIESNk3rOGMQYvLy+cPXsWQOmMKZGRkWjevLlM21V01R3q86khb2UJRzU1NSQnJ9d46AljDN988w2uXbuGhIQEbNmyRWzIB6kaaZ2Pj3F1dUVYWBgAyLxnkVAoxPLly7Fu3TpuWatWrfD1118jNDQURUVF2LBhAzZv3lzh41+9egV/f38ApcNRJ0yYINN4CamLKLFCCCFEIaWkpGDVqlU4cOCA2DfELVu2xOrVqzF27FiZfBjmW1mxQQBKUycmPDwcK1asAFBaByQ0NFSmSRWg9MO/hYUFLCwsKlzPGENGRsZHEy8fKw6clZWFrKws3Lt3r8L1WlpaMDc3rzTxUlGRXcYYrl69Cl9fX4SHh4v1uFFRUYGTkxO8vb3Rs2dPuSUL165di3379gEoHS5w8uRJdOrUSS5tK6KaDvX5GMYYEhMTAZT2QqrN3y0VFRXs3LkT1tbW3AxcLi4uVMi2GqR5PhTBmzdvMG7cOFy6dIlb5uTkhICAAKSnpyMsLAyMMWzZsgUaGhpYtGgRlwgsK4js7u6ODx8+AADGjBlDUysTUgOUWCGEEKJQ3r17hw0bNuDnn38W63FgZGSEZcuWYerUqWIFXuuaBw8ecLdrMh2rvD19+hSurq7c/XXr1inENMsqKiowMjKCkZFRpdPS5uXlITk5mUu0/Df58urVKwgEggofW1RUhISEBK4mSUXKiuyamZmhsLAQDx48EJu9CigdMjVx4kTMnj1b7om0gIAALFu2jLsfGBiIfv36yTUGRSCNoT4fk5SUxF20tm3bttbxdurUCTNnzsT27dtRUFCAuXPnig3jIB8n7fPBpz///BNjxozB69evAZT2wNm4cSO8vb2hoqICXV1dbN68GfPnzwcArF+/Hn5+fhg0aBAaN26M27dvIy4ujtufhYUFtmzZwsuxEKLsKLFCCCFEIeTl5WHHjh3YtGkT96EXKB2a8OOPP2LOnDlyq3vBp7///htA6ZTRil6I9/3793B0dOTqFTg7O2PBggU8R1V1Ojo6aNu2baUXV0KhEKmpqZX2enn58uVHi/N+qsiupqYmzMzMEB8fj82bN8u1yG5UVBSmTJnC3d+0aRPGjRsnk7YUkbSH+nzM9evXuds2NjY13k95K1aswKFDh/DmzRucOnWKCtlWgyzOh7wxxrBt2zYsWLCASwSampri8OHDEvXGvL29IRKJuL/NeXl5OHbsmMQ+27dvj4iICBgZGcn+AAipgyixQgghhFfFxcXYv38/Vq1aJVZfREtLCz/88AMWLVoEQ0NDHiOUn9evX+Off/4BUDoF6H+LISqS4uJijBgxgou3Q4cOCAgIqFP1btTU1GBmZgYzMzP07Nmzwm3ev38vkXB5/PgxYmNj8ebNm4/O7FRcXIwnT57gyZMnlbYviyK7sbGxcHZ25i7IZs6cyX2jXdfJYqjPp5QvuG1nZyeVferq6mLLli0YP348ACpkWx2yOB/ylJ2djYkTJ4rN/GNnZ4dDhw7BxMREYnsVFRX8+OOPGDhwIH755ReEhIQgNzeXW29jYwMvLy98//33Cv0/hxBFR4kVQgghvBCJRPjtt9+wbNkyPH/+nFuuqqoKDw8P/PTTTzA3N+cxQvkrKyAKyL7YYW0wxjBp0iRcvnwZAGBoaIhTp059Fj2K/qtx48Zo3LgxOnbsiBs3buDy5cuIjIyESCQS265nz57o06cP6tWrJzHsSJ5Fdp8/f47BgwcjLy8PADBy5Ehs27atTiXE/kvWQ30+pqSkBGfOnAEA1K9fv9IEXU24uLhg3759VMi2GmR5PuThwYMHGDlyJOLj47llixcvxqpVqz7Zu61jx47YvXs3Nm/ejFevXqGwsBD6+vqf3f9ZQmSFEiuEEELkijGGqKgoLF68WGxsN1B6kbd69Wq0a9eOp+j4dfDgQe72kCFDeIzk45YuXYrQ0FAAgLa2NsLDw9GqVSueo+KHQCDAiRMn4Ovri5s3b4qtq1evHtzd3TFnzhy0bt26wsfLs8iusbExzp8/j3fv3gEo/aZ6//79Sl+8syLyHOrzMefOneOe7yFDhki1RwAVsq0+WZ4PWQsODsb06dO5WcR0dXUREhKCoUOHVms/Ojo6aNOmjSxCJOSzRokVQgghcnP9+nUsXrwYV69eFVver18/rF+/Ht27d+cpMv49e/YMf/zxBwCgTZs2Cjv2f/369dyUnioqKjh48CC+/vprnqOSv+zsbBw4cAA7duzAy5cvxdaZmJjghx9+wLRp0z45jI3PIruxsbHQ09PjiuxW1utFT09PaXq08DHU52N27drF3XZ3d5f6/qmQbfXI+nzIQmFhIWbPns3N3gUAXbp0wbFjxyqdFY0QIn+UWCGEECJzDx8+xJIlS7gu2GVsbGywYcMGhZhFpjIikQgqKioyv7D09fXlbnt4eCjkhayvry98fHy4+35+fnBycuIxIvlLSkqCn58f/P39uaK9ZTp27Ih58+bh+++/l2qtC76L7DZo0OCjiRdzc3NeX698DvX5mFu3buHixYsASmdbsbe3l0k7VMi2auR1PqQpMTERzs7OuHPnDrdsypQp8PPzk5jOnRDCL0qsEEIIkZkXL17gp59+QkhIiFgRz9atW2Pt2rUYOXKkQiYQyly6dAlDhgyBqqoqGjduLLN2RCIRUlNTAZQOrSk/W4ui8PPzw7x587j7GzduxA8//MBjRPJ1+/ZtbN26FceOHZO4cB80aBC8vb3Rv39/Xl7PHyuyyxjDjBkzsGfPHgClSYbZs2dz9VvKEjCpqamVFtrNzc3F48ePK+wBApQmfmr6/ijf0yYpKanKj1OUoT4fi6/8DFkLFy6U2ZCr/xaydXR0RJMmTWq0r5qeD0Unz/MhLefOncP48eO517a2tjb27NkDNzc3niMjhFSIEUIIIVKWlpbGZs6cyTQ0NBgA7qdZs2bM39+flZSU8B1ilQwePFgsfnn8mJqa8n3YYkQiEVu+fLlYjKtWreI7LLkQCATsxIkTrFevXhLnSUtLi02ePJk9fPiQ7zA/au3atVzM6urqLDo6usLtioqK2LNnz9jly5dZYGAgW7VqFZs0aRL79ttvWevWrZm2trbMX/sGBgafPJ7Xr1+zTZs2sfbt21e4D3Nzc7Z06VL29OlTaT+V1RIaGsrF1KpVK1ZUVCTT9kQiEevdu7fcz4eykPf5YIwxFxcXrs34+PgqP04gEDAfHx+xc9GqVSsWFxcnw2gJIbVFPVYIIYRITXZ2NrZs2QJfX19u1hGgdOYSHx8feHl5KU2xQPZ/34gDpTMVmZiYyKQ3gkAg4KaZVlFRwcqVK6XeRk0JhUJ4eXlh79693LLly5dj6dKlPEYle7m5uQgMDMT27dvx7NkzsXVNmjSBl5cXPD09YWRkxFOEVRMUFCQ2S0xAQEClw+40NTVhYWFRac0GVkmR3ZiYGCQmJtb4vVH+9d++ffsKt1HUoT6VSUlJwaxZs7j7vr6+0NTUlGmbKioqOHbsGNzd3REXFyfT86Fs+DgfNfXmzRuMGzcOly5d4pY5OTkhICAAurq6PEZGCPkkvjM7hBBClF9BQQHbunUrMzAwEPuWrX79+mzJkiUsKyuL7xCrLTk5mTuOAQMGyKQNkUjEvv32W64dHx8fmbRTE1lZWczBwUHsfO7YsYPvsGQqOTmZLVy4kDVu3Fji2/t27doxf39/lp+fz3eYVXL+/Hmmrq7Oxb9hwwa+Q6pQfHw8F6OLiwu3XCQSsVu3brEZM2YwPT29CntU9OrVi+3fv599+PCBxyMQV1RUJNZzZPTo0XyHVC2VnQ9lxef5qG6PlWvXrrGmTZtyj1FTU2NbtmxhIpFIDtESQmqLeqwQQgipMYFAgODgYKxYsQLJycnccnV1dUybNg1Lly6FiYkJjxHWXGxsLHdbVjP0HDlyBNHR0QCA5s2bi/Uu4NPjx4/h6OiI+Ph4AKXnMygoCOPGjeM5Mtm4e/cufH198dtvv0nMrjNgwAB4e3vju+++470nRFXduXMHI0eO5I7Fy8tLrL6EIlO0WX2qgzGG6dOn49q1awBKY/3ll194jurzpSzngzGG7du348cff+R6Y5mamuLw4cPo3bs3z9ERQqqKEiuEEEKqjTGGkydPYsmSJfj333+55SoqKhg3bhxWrlyJL7/8kscIa0/WiZXk5GR4enpy97dv34769etLvZ3qYIwhODgYP/zwA3JzcwEABgYGOHz4MPr3789rbNImEokQERGBrVu34sqVK2LrNDQ0MG7cOHh7e6NTp078BFhDiYmJGDx4MHf+nJycsGPHDoUuEl3m8uXLMDc3V/ihPhVhjGHu3LkICAgAUFpo9OjRo9DX1+c5ss+TspyP7OxsTJw4EcePH+eW2dnZ4dChQ0r7pQQhnytKrBBCCKmWy5cvY9GiRRJTszo4OGDt2rXo3LkzT5FJV/nESteuXaW6b6FQKDbbg7OzMxwdHaXaRnWlp6dj2rRpOHXqFLfsf//7H06ePImWLVvyFpe05efnIzg4GNu2bcPTp0/F1unr68PT0xNeXl4wNTXlKcKay8zMxKBBg7gaGba2tggLC1PI2U/Y/9Uw2rFjB7fs9evXYtvwOatPdZSUlGDatGncRbyKigqCg4Px1Vdf8RzZ50lZzseDBw8wcuRIrmcgACxevBirVq2CujpdohGibOhdSwghpEpiY2Ph4+ODCxcuiC23tbXF+vXr61SXZVaucK2enp7UEwtr1qzBH3/8AaC0e/q+fft461EgFAoREBAAHx8fZGRkcMvd3Nywe/du3nvRSEtaWhp27dqFX375BZmZmWLrLC0tMXfuXLi5uSnt8RYUFGDo0KF48uQJAKBNmzY4ffq0whWLVuahPhVJS0vDmDFjcPXqVQClF/EHDhzAqFGjeI7s86Qs5yM4OBjTp09HQUEBgNIps0NCQjB06FCeIyOE1Bhv1V0IIYQohSdPnrDRo0dLFI60srJi4eHhdbKwniwL1x45coTbt6qqKrt69apU919VIpGIXbx4kXXu3FnsvBoaGrITJ07wEpMs3L9/n3l4eDBNTU2J17CdnR07c+YMEwqFfIdZKwKBgDk6OnLHZWJiwhITE/kOi1NYWMiOHj3KHBwcmJqaWqXT+/bv319pzoVIJGJHjx5lhoaGXPyamprsyJEjfIdWK8pavFYRz0dFxWsLCgrY1KlTxV73Xbp0Yc+ePeMtTkKIdFCPFUIIIRVKSUnBqlWrcODAAbGaBy1btsTq1asxduxYhRxiIA2yqq8SExMDNzc37v66devk3tNHIBDg7Nmz2LhxI/7++2+xdaNHj4afnx+MjY3lGpO0McZw/vx5+Pr6csWBy6irq2PMmDGYO3euzIoSyxNjDLNmzeKGcDVo0ACRkZG8D99i/9frKzAwEIcOHeKGvZXXq1cvDB48GD4+PgAAExMThayf8l93797FokWLxHrvNW3aFMePH8fXX3/NY2SfJ2U5H4mJiXB2dsadO3e4ZVOmTIGfnx+0tbV5jIwQIg2UWCGEECLm3bt32LBhA37++WcUFhZyy42MjLBs2TJMnToVmpqaPEYoe7JIrLx48QLDhg3jun67ubnJbaYWkUiE27dv4+TJkwgODkZqaqrYemtra2zfvl3ph3MVFhYiLCwMvr6+EsNMdHV1MW3aNMycORNmZmY8RSh9GzduxO7duwGUJo1OnDiB//3vf7zFU92hPgkJCVxiRZEJhUJcunQJfn5+OHv2rNg6R0dH7Nu3D02aNOEpus+Psp2Pc+fOYeXKlVyCUVtbG3v27BFLtBNClBslVgghhAAA8vLysGPHDmzatAkfPnzgljdq1Ag//vgj5syZgwYNGvAYofxIu3BtamoqrK2tuQ/VlpaWWLlyJdLS0sAYk/gBUOHyqq4rKCjAixcv8PTpU9y+fRvXr19Henq6RFxWVlZYtGgRxo4dqxQ9BSqTkZGB3bt3Y9euXWJ1YgDAwsICc+bMgYeHR517/YaEhGDx4sXc/V9//RXffvut3OMoKipCeHg4AgMDERUVpZSz+lQkMzMTN27cQFRUFE6dOoWUlBSx9c2bN8e2bdvg5OSkFLMuKTtlPh9z5szhbrdq1QrHjx9XuhnHCCEfp8LKPokRooSysrIkPsDJgo6OjsIVACTkY65evYrjx49X6f0hFArx+PFj3L59m+tNAQBqamro2LEjrK2ta/z619DQgI6ODoyNjdGyZUu0b98eX3zxhUJfWDHGYGJigvT0dOjp6SEzM7NWH9IZYwp1vKqqqrCysoKjoyNcXV3x5ZdfKlR8H5OSkoJu3brBw8MDa9euxT///INt27YhODgYRUVFYtva2trC29sbw4cPr5ND1qKjozF48GAIBAIApcPKyidZZK2qQ30+NatPQkICV6TW0tIS9vb2Mo27Ih8+fEBoaCjatGmDLl26IDU1FQkJCRIX7mXMzc0xf/58TJs2DVpaWnKOVrbofEiPq6srwsLCxJY5OTkhICAAurq6PEVFCJEVSqwQpcQYw9ChQ3Hu3Dm5tamtrQ0TExO0bdsWHTp0gK2tLXr37g1DQ0O5xUBIVeTk5MDU1BR5eXl8h1IhfX192NraYvDgwXB0dISJiQnfIYl59eoVzM3NAQADBgyQqNFRXfHx8WjdurU0QpMJRT8f5ZVPcJmamkoMaVJVVYWzszO8vb0VbmpVabp37x769OmDnJwcAICnpyd27doll2/ppT2rz7Nnz9CqVStZhCpVGhoa+O677+Du7o5hw4ZBQ0OD75Bkgs6H9IwfPx6hoaEASr+o2LhxI7y9vRWuNw0hRDoosUKUUm5uLvT09Lhv6vhka2sLZ2dnjB07VukLPpK6ofw3jopOTU0NAwcOxMyZM2Fvb68QHzhPnz4NR0dHAMDChQuxYcOGWu2Pzod0FBcXo379+hX2wmrYsCGmTJmCmTNn8l60VdZevHiBHj16IC0tDUBpPYljx47JtFeOLIf6iEQi2NjY4N69e1KOunYMDAzQrl07dO/eHb169cKAAQPQsGFDvsOSOTof0nPkyBGMHTsWpqamOHTokNLXsCKEfBwlVojSWrRoETZu3Mjd/+KLL9C+fXupt8MYQ15eHjIzM5GUlITs7OwKt9PU1MSYMWMwc+ZMdOvWTepxEFJV5S/kBw4ciNWrV3Pr4uLisGvXLty9e1fsMV27dsUPP/yADh06SC0OxhhKSkqQk5ODtLQ0JCQkIC4uDjdu3MDbt28ltu/SpQvWrVuHgQMHSi2Gmli+fDn3nB05cgSjRo2q1f4+dj7kSVnPR2ZmJvbu3YudO3dK9FABSi/qAwMDMXr0aB6ik693797B1tYW//77LwCgR48e+P3332UyVFVaQ32qQigU4v79+3IZ2luZjIwMmJqaomHDhjA2Nq5z9Xiqg86H9KSlpcHQ0BDq6lTWkpA6T6aTORMiQ0KhkLm5uTEADABr0KABu3fvnkzbFIlELCUlhZ05c4bNnz+ftW/fnmu//I+9vT27e/euTGMhpDLx8fHca9HFxYUxxtiDBw/YsGHDJF6rNjY2LDo6Wq7xCYVCFhMTw3x8fJi5ublETEOHDmUvX76Ua0zlDR48mIvl+fPntd5fRedDkSjq+Xj69CmbMWMGq1evXoV/Z//74+PjwwQCgdzjlJf8/Hxma2vLHW/r1q3Z27dvpd7O69ev2aZNmyr9/2Zubs6WLl3Knj59KvW2CSGEEGVFiRWi1EpKSsQuFr/44guZfND8mMePH7MFCxYwfX19sQ+fKioqzNXVlb1+/Vqu8RBS/kJ++PDhbMKECUxFRUXs9dm6dWt29OhRJhKJeI1VIBCw48ePM2tra7H4GjVqxMLCwuQej0gkYkZGRgwA09PTk8rzo+iJlfL4Ph8ikYhduXKFDRs2TOI1q6KiIpb4iYmJYU5OTmLb9OvXj6Wlpck8TnkTCARsxIgR3HEaGxtLJelXprCwkB09epQ5ODgwNTU1iWRKvXr1mKurK7t48SITCoVSa5cQQgipKyixQpRefn4+69atG/cB8Ntvv2UlJSVyjyMvL4/5+/uzFi1aiH0gbdy4MQsMDOT9ApZ8PspfyKuqqoq9Hps1a8b8/f15eY98jFAoZAcPHmRNmzYVi3fWrFlyjTU5OZlre8CAAVLZpzIlVsrI+3wUFxezsLAwZmNjI3FRr6Ojw2bOnMkSEhKYi4sLtzw+Pp6JRCK2ZcsWsWRA06ZN2bVr16QeI19EIhH74YcfxHpnxsbGSmW/t27dYjNmzGB6enoV9k7p1asX279/P/vw4YMUjoQQQgipuyixQuqE5ORk7ltmAGzx4sW8xVJYWMh8fX0lerAMHDiQpaam8hYX+Tx8+PCBeXl5SVwg6enpsc2bN7P8/Hy+Q/yo9+/fs/Hjx4vFPnz4cFZQUCCX9k+dOsW1u3DhQqnsUxkTK2VkfT6ysrLYpk2bmJmZmcRrtlmzZmzjxo3s3bt33Pb/TayU+eOPP5iJiQm3Tk1Njfn6+taJhPbGjRu541JXV2dRUVG12h8N9SGEEEKkjxIrpM74448/mLq6Otdl/K+//uI1nrdv3zJXV1exD6ympqbs6tWrvMZF6qaCggK2detWZmBgIPaaU1NTY0uWLGFZWVl8h1gt+/btYxoaGtxxDB48mBUWFsq83WXLlnFtHjlyRCr7VObEShlpn49nz56xWbNmMR0dHYkL+y5durDQ0FBWXFws8bjKEiuMMZaamsrs7OzE9jVy5Eil7m0RGhoqdjyBgYE12g8N9SGEEEJkixIrpE7ZsGED90GxVatWLDc3l++QWHh4ODM1NRW70N2yZUud+CaV8K+kpIQdOHCgwqKjANiIESP4DrHGoqOjxS68x44dK/P3jbQL1zJWNxIrjNX+fIhEIvbXX3+xkSNHSgxRA0qL5F65cuWj+/xYYoWx0vfDokWLxPZraWnJ7t+/X6Nj5tPFixfFkllr1qyp1uNpqA8hhBAiP5RYIXWKQCBgPXr0EKsHoAjevHnD+vXrJ/aBdsqUKQpX54IoD5FIxI4fP87atm0r9rpSUVERK+iszBfyjJX2RCs/K0x1Ly6rQxaFaxmrO4kVxmp2PkpKStjhw4fZV199VWFPCU9PT/bkyZMqtf+pxEqZ06dPM11dXbF2goKCqnycfLt37x5r2LAhF/+0adOq/HqkoT6EEEKI/FFihdQ5T58+5T74q6qqskePHvEdEmOsNOmzZMkSsQ+4Dg4OCtGrhiiXS5cuse7du0tcMDk4OLB79+7VqQt5xkrrnpTNEKOqqsquXLkik3ZkUbiWsbqVWGGs6ufjw4cPzNfXV6KgNwBmYmLC1qxZwzIyMqrVdlUTK4yVDjfq0qWLWLtTp06VW72emnrx4oVYL8dhw4Z9MglPQ30IIYQQfqmCEB4IBAKZ7dvS0hJLly4FAIhEIvz4448ya6s61NTUsGbNGhw8eBAaGhoAgHPnzqFfv37IysriOTqiSCp7f8TGxuK7775Dv379cOvWLW65ra0trl69irNnz6Jz587yClNuhg8fjpUrVwIofU9PnDgReXl5Um8nNjaWu21jYyP1/dcVnzofSUlJmD9/PszNzeHt7Y2XL19y6zp27IjAwEC8ePECS5YsgaGhoczitLCwwPXr1zF58mRu2b59+2Bra4vExESZtVsb7969w6BBg5CamgoA+Prrr3Ho0CGoq6tLbMsYw+3bt+Hl5QVTU1OMGjUK586dg1Ao5Lbp1asX9u/fj7S0NISEhKB///5QVaWPfoQQQoi0qTDGGN9BkM9LSEgIpk+fDlVVVTRq1AgqKipSb4Mxhjdv3nAfMJctW4ZVq1ZJvZ2aunz5MhwdHZGdnQ2g9CIuOjoaenp6PEdG+FbR+6OkpAQ5OTkoKCgQ21ZdXR2NGjWCtra22PtIIBDgzZs3AIDevXvj6tWrcj0GWRAKhejbty+uXbsGAFi8eDHWrVsn1TaWL1+O1atXAwB+++036OnpYc+ePTh79iw0NTWhq6tbo79Xn8v5cHJywtatW3Hs2DGxi3sAGDRoELy9vdG/f/9a/c13dXVFWFgYACA+Ph6tWrWq0uMCAwPh6emJwsJCAICenh5CQkLg4OBQ41ikrbCwEPb29txzamlpievXr0skn1JTUxEaGorAwEA8fvxYYj/m5uZwc3PDhAkTYGlpKZfYCSGEkM8dJVaIXJ09exaOjo4SH7plrVGjRvjw4YNc2/yUBw8eYMCAAUhPTwdAyRVS2oNp+PDhUn1/GBgY4O3bt1LbH5/i4+NhZWWF4uJiaGlp4enTp2jevLnU9u/g4ICIiAgApRenycnJUtt3mbp2Pjp06ICSkhKoqKjgvx8ntLS0MH78eMyZMwcdOnSQSps1TawAQFxcHJydnZGQkMAt8/HxwapVq6CmpiaV+GpKKBTi+++/x7FjxwAARkZGuHHjBiwsLAAARUVFCA8PR2BgIKKioiT+RtSrVw8jR46Eu7s7+vbtS71SCCGEEDmT7FtKiIzcunULY8aM4T4Q6uvro169ejJtMy0tDUKhENnZ2Xj48CGsrKxk2l51dOzYEZcvX0bfvn2Rnp6O2NhY2Nvb4/Lly2jQoAHf4RE5u3XrFkaPHs29P7S1tblv18uoqqqiYcOG0NHR+ei3/uV7SLRv3152QcuZpaUlZs+ejc2bN6OoqAibNm3Czp07a71fxhiuXr2K33//nVtWPqmip6cHbW3tGl+s1sXzkZubi/Pnz0NHRwfv378XS6o0adIEXl5e8PT0hJGREY9RiuvcuTNiYmLg4eGBkydPAgDWrVuHv//+GwcPHoSxsTEvcTHG4O3tzSVVdHR0EBERgS+++AK3b99GYGAgDh06VOGQ0V69esHd3R2jRo1Co0aN5B06IYQQQsrwVdyFfF7i4+OZoaEhV0hvzJgxcimg5+fnx7U5adIkmbdXE48ePeJmIgHA7O3tWVFREd9hETn67/uj/BSrAFijRo3Y6tWrWU5OTpX3V/bYulAstby3b99yU/5qa2uzzMzMGu/r3bt3bMeOHaxdu3YVzp5ib2/PTpw4wYqLi2sVc106H8nJyWzhwoWscePGEs+XiooK2759O8vPz5dZ+9UpXlsZkUjEtmzZIlbktWnTpuzatWtSjrZqNm/ezMWhpqbGQkNDaVYfQgghRMlQYoXI3Js3b9iXX37JfSi0s7NjhYWFcmk7OzubNWrUiAFgDRo0kOkH/tp4+PAh09PT456j8ePHS22qV6LY3rx5wywsLCq8gNLS0mLz5s2r9swpdelCviKzZs3ijm/79u3VeqxIJGI3b95kHh4eYtMGl//56quvWEJCgtTirQvn486dO8zV1ZWpq6tXeKFf0/NRXdJIrJS5evWq2Ow7ampqzNfXV65/ew8ePCj2XHbq1Ilm9SGEEEKUEA3CJTKVm5sLBwcHPHv2DABgZWWFkydPQktLSy7tN2zYECNHjuRiiYyMlEu71dWhQwecOXMG2traAEoLmPr4+PAcFZG1nJwc9OjRA8+fPxdbrqqqikmTJiE+Ph5btmyR6cwpymjq1Knc7UOHDlXpMbm5udi3bx9sbGzw1VdfISAgQKwYcPlaLfPmzcOXX34pvYCVlEgkwtmzZ9G3b19YW1sjNDSUm7FKQ0MDbm5uiIuLE/u7WtXzoQh69+6NO3fuwM7ODkBpnRNvb2+MGjWKKywuS7///jvGjx8vtuz+/fs0qw8hhBCihOi/M5EZgUCAMWPGICYmBgBgZmaGyMhING7cWK5xjB49mrt97tw5ubZdHb169cKhQ4e4D80bNmzgijSSuoUxhrNnz6JZs2YSSZWRI0fi4cOH2L9/P8zNzXmKULF16NABnTp1AgDcvHkTKSkplW57//59zJgxA02bNsW0adNw9+5dbp2uri5mzZqFR48eidVf6tq1q+yCVwL5+fnYs2cP2rVrh6FDh+LKlSvcOn19fSxZsgQvX75EYGAgOnXqVK3zoWhMTEwQHR2NRYsWccuOHz+Orl274sGDB1XaR35+PoKCgrBo0SLMnTsXq1ev/uhjU1NT4e3tDXt7+woLVZubm2Pp0qV4+vQprl27hkmTJlH9FEIIIUTR8d1lhtRNIpGITZo0ievGrKuryx48eMBLLPn5+UxLS4sBYC1btuQlhur4+eefuedNW1ub3b59m++QiBT99ddfrE+fPhJd/bt3785u3rwplTbqwtCTT1m6dCl3jMHBwWLr8vPzWVBQEOvRo0eFQ326d+/Ofv31V5aXl8cYK/17VVbnSE9PT+pDQZTlfKSmprKlS5cyAwMDiefM0tKS7d69m3vO/utj50OapDkU6L9Onz7NdHV1xYbfBAUFVbp9bm4umz9/vtgwzvI/vXv3Zr///jtjjLHCwkJ29OhR5uDgQEN9CCGEkDqIEitEJn766SfuA6Ompia7fPkyr/HY2dlx8bx+/ZrXWD5FJBKxKVOmcPE2a9aMpaam8h0WqaUHDx6wYcOGVVjwc/PmzVJtS1ku5Gvj0qVL3DHOmDGDMcbYv//+y+bOnVvhha6Ojg6bOnUqi42NldhXcnIyt92AAQOkHquin4/79+8zDw8PpqmpKfG82dnZsTNnznzyYr+i8yELskysMMbYs2fPWJcuXcSeg6lTp7KCggKx7d69e8e6du1aYUKl/I+qqirr169fpcmXBg0asF27drEPHz5I/VgIIYQQIj80FIhInb+/P1auXMndDwkJ4caw88Xa2pq7XdXu3XxRUVHBzp07YWtrCwBISUnB6NGjudoGRLm8ePECbm5u6NSpE86cOSOxPiwsDPPnz+chMuVmY2PD3Y6Ojka/fv3Qtm1bbNu2TWxa2o4dO2L37t14/fo19u7dK/a3oExsbGyF+63LGGOIioqCvb09OnXqhICAABQXFwMA1NXV4eLigpiYGFy+fBlDhw79ZF2P8s/bnTt3ZBq7LFlYWOD69euYMmUKt2zfvn2wtbVFYmIigNJaLE5OTtwwVw0NDUyYMAHnzp3DX3/9hZUrV6JJkyYASuvUXLp0qcKpkps3b47nz59jxowZNNSHEEIIUXKUWCFSdfbsWXh6enL3fX19xWqc8KVDhw7c7SdPnvAYSdVoamri+PHjMDMzAwBcu3ZNLFlFFN+bN28wa9YstG7dGsHBwWCMSWyzZcsWjB07lofolF9mZiYaNmwIAIiPj8fly5e5dVpaWpgwYQKuX7+OuLg4eHp6fvTC9XNKrBQWFuLAgQOwsrLCoEGDEB0dza3T1dXFggULkJiYiNDQ0Go9F40aNeL+XiUkJEg9bnnS1tbGvn37EBAQwBUUv3PnDmxsbHDu3DlERUXhjz/+AAAYGRkhNjYW+/btQ35+PtatW4dVq1YhIyNDbJ+qqqpiBZKbNGmCS5cucQkYQgghhCg3db4DIHXHrVu3MGbMGK4Yn7e3N+bOnctzVKXKFwFNTU3lMZKqMzY2xuHDh9GnTx8IhUKsXbsW33zzDQYMGMB3aOQjsrOzsWXLFvj6+iIvL49b3qhRIxQUFKCkpAQAMHv2bHh7e/MVplISCASIiIjAnj17EBUVJZGsat26NaZPnw43Nzfo6+tXeb/lEyt1tXBtRkYGdu/ejV27dklc9FtYWGDOnDnw8PBAgwYNatxGixYt8OrVK7x9+xaFhYVcUkJZubu7o0uXLnB2dkZCQgKysrIwZMgQsRmj5s2bhz179uDQoUMV9krR0dFBXl4eRCIRkpKSAAD169fHuXPnaOYpQgghpA6hxAqRioSEBDg4OCA/Px8AMGbMGGzevJnnqP4/IyMj7vbbt295jKR6evbsiXXr1mHhwoVgjMHFxQX37t2DqalpjfaXnZ0Nf39/5OTkoEWLFmjevDlatGgBMzMzpb8I4lthYSF2796NdevWITMzk1tev359uLu74/Dhw9wUrqNGjYKvry9UVFT4CleppKSk4MCBA/D398erV68q3Obo0aMYOXJktZ9Txhhu3LgBANDT00PLli1rG65C+eeff7Bt2zYEBwejqKhIbJ2trS28vb0xfPhwqKmp1botAwMD7nZWVlaN/04pks6dOyMmJgYeHh44efIkAODZs2cASodMLVy4UOIx5ubmcHNzw4QJE3DlyhWx6cHV1NRw9OhRdOvWTT4HQAghhBC5oMQKqbX09HQMHDiQS1jY2dkhKCjok2Py5UlTU5O7XVZHQFnMnz8fFy5cwO+//4709HS0adOmxuPxs7OzkZOTU+E6ExMTNG/enEu2/Pe3np4eJQIqIBAIEBwcjBUrViA5OZlbrq6ujmnTpmH69OlwcnLiki19+vRBcHCwQr0/FJFIJMLFixexZ88enDlzRmJa2pYtW6Jhw4ZczaSZM2dizpw51W5HIBBwPQ2EQmGdeI0zxnDp0iVs3boVkZGRYutUVVXh7OwMb29vfPXVV1Jtt169etxta2vrGidrCgoKkJubiwYNGojtEwDevXvH3Y6MjMTMmTNrFmw16Orq4uDBg5g4cSIOHTrELS9f96pevXoYOXIk3N3d0bdvX+79/f79e7F97d27F4MHD5Z5zIQQQgiRL0qskFrJzc2Fg4MD9w2elZUVTp48CS0tLZ4jq1xFtS4U2du3b/Ho0SPufk5OTqXJkdpIS0tDWloabt26VeH6Bg0afDTx0rRpU6irfz5/UhhjOHnyJJYsWYJ///2XW66iooJx48Zh5cqVMDExQb9+/biaE+3bt8epU6eod9BHZGRkICAgAHv37sXz58/F1qmqqmLIkCGYPn067O3tMW7cOC6xkpaWVuu2s7OzERkZiUGDBtV6X3woLi7GoUOH4Ovri/v374uta9iwIaZMmYKZM2fKrFdO+b+t0jgf5ZMoFdm/f79MEyuMMcTExCAwMBBhYWH48OGDxDa9evWCu7s7Ro0aVWHCu2zoHwB0794dkyZNklm8hBBCCOHP53MVRKROIBBgzJgx3MwIZmZmiIyMROPGjfkNrAJlQzCA0m8flYVIJIKbmxt3kaKjo1Pr51cgEEBdXR0DBw6Evr4+kpKS8PLlSyQlJSE1NbXSxFNubi4eP36Mx48fV7heTU0NzZo1qzDxUna7NvUbFMnly5exaNEiiSSUg4MD1q5di86dO0MgEMDJyYnbpmnTpoiMjISenh4fISs0xhiuXbuGPXv24NixY2IXowBgamqKKVOmYPLkyWL1ksq/r01NTWvcCygvL4/rWTBr1iw8fPhQoZPD/5WZmYm9e/di586dEjWkmjdvjtmzZ2PSpEky/9snrfPxqR4rBQUFAIDJkyfXPNiPSE1NRWhoKAIDAyv9eweUzgZ06tQpsSFQ/1U2fAiAQhRyJ4QQQohsUGKF1AhjDNOnT0dERASA0mRFZGQkNyuEonnz5g13uzpFLfm2evVqREVFASgtZhsXFwdjY2OZtVdcXIxXr16JJVv++7uwsLDCxwqFQiQlJSEpKQl//vlnhdvo6elV2Nul7LeRkZFCD5GJjY2Fj48PLly4ILbc1tYW69evR+/evQGUvj+8vLxw9uxZAKWFayMjI8VmBSGldThCQkKwZ88e/PPPPxLr7e3tMX36dAwZMgQaGhoS68sSjmpqakhOTq7x0BPGGL755htcu3YNCQkJ2LJlC5YsWVKjfclTfHw8tm/fjoCAAC7ZUKZ79+6YN28eRowYIbeeZNI6Hx/j6uqKsLAwAJBqz6KioiKEh4cjMDAQUVFREkPPyjRt2hR9+/ZFWFgYSkpKsGHDhkrrib169Qr+/v4ASoejTpgwQWrxEkIIIUSxUGKF1MjKlStx4MABAKUfGE+dOgUrKyueo6pc2VAlAEozE0N4eDhWrFgBoHQIRGhoqEyTKkDpubSwsICFhUWF6xljyMjI+Gji5WPFgbOyspCVlYV79+5VuF5LSwvm5uaVJl74KrL79OlTLFu2DEeOHBFbbmVlhfXr18PBwUGsNsfatWuxb98+AKXfap88eRKdOnWSa8yKijGG27dvY8+ePfjtt98kEgKGhoaYOHEipk6d+tH3KmMMiYmJAEp7ZdTmIl5FRQU7d+6EtbU1NwOXi4uLQhayZYzh6tWr8PX1RXh4uFgPMxUVFTg5OcHb2xs9e/aUa70YaZ4PeSk/1KeyWX3Kc3JyQkBAANLT03Hw4EEwxrBlyxZoaGhg0aJF3FCgsoLI7u7u3PChMWPG0NTKhBBCSB1GiRVSbf7+/li5ciV3PyQkBHZ2dvwFVAVldRgAwNLSksdIqubp06dwdXXl7q9bt04hpllWUVGBkZERjIyMKp2WNi8vD8nJyVyi5b/Jl1evXokVfSyvqKgICQkJXE2SisizyG5KSgpWrVqFAwcOiH2D3bJlS6xevRpjx46VuIAMCAjAsmXLuPuBgYHo16+fVOJRZrm5uTh48CD27NmDu3fvSqzv06cPpk+fjhEjRlRpGE5SUhJ30dq2bdtax9epUyfMnDkT27dvR0FBAebOnSs2jINvJSUlOHr0KHx9fcWmhwZKhwhOnDgRs2fP5i1xLO3zIUufGupjZGSE/Px85ObmAijtgbNx40Z4e3tDRUUFurq62Lx5M+bPnw8AWL9+Pfz8/DBo0CA0btwYt2/fRlxcHLc/CwsLbNmyRT4HRwghhBBeUGKFVMvZs2fh6enJ3ff19VWKceN///03gNKZWjp37sxzNB/3/v17ODo6cvUKnJ2dsWDBAp6jqjodHR20bdu20osroVCI1NTUSnu9vHz58qPFeeVRZPfdu3fYsGEDfv75Z7GhT0ZGRli2bBmmTp0qNtNUmaioKEyZMoW7v2nTJowbN+6jbdV19+/fx549exAaGipxXnV1deHm5oZp06ahffv21drv9evXuds2NjZSiXXFihU4dOgQ3rx5g1OnTilEIdv379/D398ffn5+ElNNN2vWDLNmzcKUKVN4r90ji/MhTZ8a6lM2q4+Ojg78/f0hEokAlNaKOXz4MDfMr4y3tzdEIhH3tzkvLw/Hjh2TaLd9+/aIiIiAkZGRjI6MEEIIIYqAEiukym7duoUxY8ZwH0i9vb0xd+5cnqP6tNevX3P1G6ytrSWKISqS4uJijBgxgou3Q4cOCAgIqBNTwJZRU1ODmZkZzMzM0LNnzwq3ef/+/UeHG8mqyK6hoSHOnj2LHTt2iM0A0qhRI/z444+YM2dOpQV4Y2Nj4ezszL0/Zs6cyX2j/bkpKCjA0aNHsWfPHty4cUNifffu3TF9+nSMGTMG9evXr1Eb5evcSKvHnK6uLrZs2YLx48cD4LeQ7fPnz7Fjxw4cOHAAeXl5Yuu6dOmCefPmYfTo0RXWnuGDLM5HbVVlqE/ZrD7fffcd5syZg9DQUG6dnZ0dDh06BBMTE4nHqaio4Mcff8TAgQPxyy+/ICQkhOvhApQml7y8vPD9998r9P8cQgghhEgHJVZIlSQkJMDBwQH5+fkASseLV1awT9GUFRAFpFvsUNoYY5g0aRIuX74MoLTWxKlTp+rMTDrV0bhxYzRu3LjSuiSyLrJbRlVVFZ07d8bw4cPRpk0bPHr0qMIiu8+fP8fgwYO5C+CRI0di27ZtdSohVhVPnjzB3r17ERgYKHERq6OjAxcXF0ybNg3W1ta1aqekpARnzpwBANSvX7/SBF1NuLi4YN++fbwUsi2rzeHr64uTJ09yvSbKDB06FPPmzUOfPn0U6rUly/NRE58a6mNubg43NzdMmDABlpaWePDgAfr164f4+Hhum8WLF2PVqlWf7N3WsWNH7N69G5s3b8arV69QWFgIfX19sdmrCCGEEFL3UWKFfFJ6ejoGDhzIFSW1s7NDUFCQQs/eUt7Bgwe520OGDOExko9bunQp922ptrY2wsPD0apVK56jUkyyLrJbRiQS4e7duxI1QcoX2TU2Nsb58+fx7t07AKXfVO/fv18pindKQ3FxMU6dOoU9e/ZwScHyOnbsCE9PT7i4uHDFPWvr3Llz3PM9ZMgQqfYI4KOQrUAgwIkTJ+Dr64ubN2+KratXrx7c3d0xZ84ctG7dWmYx1IYsz0dVVXWoj7u7O/r27cv9/woODsb06dO5Isq6uroICQnB0KFDq9W+jo4O2rRpI52DIYQQQojSocQK+ajc3Fw4ODhws+pYWVnh5MmTvHSNr4lnz57hjz/+AAC0adNGIcf+A6XFD9etWweg9MLu4MGD+Prrr3mOSnl9qsguYwynTp2Cj48P/v33X7F1hoaG0NTURHp6eo2K7MbGxkJPT0+uRXb5kJiYCH9/fxw4cADp6eli67S0tDBmzBhMnz4dX3/9tdSPc9euXdxtd3d3qe4bkF8h2+zsbBw4cAA7duzAy5cvxdaZmJjghx9+wLRp02BoaCj1tqVJ1uejMmUzTFVlqM+oUaPEEnuFhYWYPXs2N3sXUDrE6tixY5UmbAkhhBBCKkOJFVIpgUCAMWPGICYmBgBgZmaGyMhING7cmN/AqsHX15e77eHhoZAXsr6+vvDx8eHu+/n5wcnJiceI6rbr169j8eLFuHr1qtjyfv36Yf369ejevTsA/ovsmpubK9zrVSAQICIiAnv27EFUVJREnZvWrVtj+vTpcHNzg76+vkxiuHXrFi5evAigdLYVe3t7mbQjy0K2SUlJ8PPzg7+/P1ekukzHjh0xb948fP/990qRwJbX+ajI4MGDK0xu/neoz38lJibC2dkZd+7c4ZZNmTIFfn5+vEznTgghhBDlp8IqqwBJPmuMMUyZMgUHDhwAUNo9+s8//4SVlVWN91m+q/aFCxegqakJXV1dmV08ikQipKamAigdWpOSkiKzi72a8vPzw+zZs7n7GzduVKoZgJTJw4cPsWTJEq4WRBkbGxts2LChWtNZM8YwY8YM7NmzB0DpMIPZs2dz9VuqUmT3U3R0dGqcxBQIBHjz5g0AoHfv3hJJpOpKSUnBgQMH4O/vLzEzjbq6OkaMGIHp06fDzs5Opskgxhj69u3L9ULbu3cvpk6dKrP2QkNDuUK2mpqaaNKkSY32U/58GBoaIisrS2KoyqBBg+Dt7Y3+/fsrXEKtMvI8H2X/P2bPno3Xr19LrK9sqM9/nTt3DuPHj+d6t2hra2PPnj1wc3OTSdyEEEII+UwwQirw008/MQAMANPU1GSXL1+u0X5EIhG7desWmzFjBtPT0+P2Ke8fU1NT6T5BtSQSidjy5cvFYly1ahXfYdVJiYmJbMKECUxFRUXs+W7dujU7evQoE4lE1d7n2rVruf2oq6uz6OjoCrcrKipiz549Y5cvX2aBgYFs1apVbNKkSezbb79lrVu3Ztra2jJ/7RsYGNToeRMKhez8+fPMycmJqampSey3ZcuWbN26dSwtLa1G+6+J0NBQrv1WrVqxoqIimbYnEolY7969ZXZutLS02OTJk9nDhw9lehyyIuvzUZX/H7169WL79+9nHz58+Oi+BAIB8/HxEXtsq1atWFxcnFRjJoQQQsjniXqsEAn+/v5i3zoePnwYo0ePrtY+PjUrg4GBATQ1NWVWALf8N8QqKirYu3cvpkyZIpO2qksoFMLLywt79+7lli1fvhwrVqxQmm+qlcGbN2+wdu1a7NmzByUlJdzyZs2aYcWKFXB3d//kjB8VCQoKEqsjERISAldX1xrFyCopshsTE4PExMQavx5q02MlIyMDAQEB2Lt3L54/fy62TlVVFUOGDMH06dNhb28v1wK9KSkp6NSpE1ck9cyZM9UuMFoT6enpcHd3R1xcXLXOh0gkQn5+PnJzcyV6pzRp0gReXl7w9PSEkZGRtEOWC1mej0/9/ygTHR1dpZ5mb968wbhx43Dp0iVumZOTEwICAqCrqyuVmAkhhBDymeM5sUMUTHh4uNi3076+vlV+bGFhITt69ChzcHCo8BvuevXqMVdXV3bx4kUmFApldgwikYh9++23XLs+Pj4ya6u6srKymIODg9jzsmPHDr7DqlM+fPjAli1bxnR0dMSeZz09PbZ582aWn59f432fP3+eqaurc/vcsGGDFCOXnvj4eC5GFxeXT24vEonYH3/8wcaOHcs0NDQq7PG1fPlylpSUJIfoJRUVFYn1HBk9ejQvcVRFcnIyW7hwIWvcuHGFPSy++uqrWr0GFYEszkdV/3/079+fWxYfH//J/V67do01bdqUe4yamhrbsmVLjXqqEUIIIYRUhhIrhHPz5k1Wv3597gOot7f3Jx8jza7a0vLbb79xbTdv3pzl5eXJpd1PefToEbO0tBQbQhIWFsZ3WHVGQUEB27p1KzMwMBB7/dWvX58tWbKEZWVl1Wr/sbGxrEGDBtx+vby8FPbirKqJlXfv3rEdO3awdu3aVfjetbe3ZydOnGDFxcVyjF6cSCRiHh4eXEzm5uYsMzOTt3gqc+fOHebq6iqWeCv76dmzZ7USXYpMmuejJv8/XFxcqpRYEYlEzNfXVyxJY2pqyq5evVqjWAkhhBBCPoYSK4QxVnohZmhoyH0AHTNmzEd7lbx+/Zpt2rSJtW/fvsIPw+bm5mzp0qXs6dOncjwKxpKSksQ+oJ84cUKu7VdEJBKxwMBAsYtyAwMDdvHiRb5DqxNKSkrYgQMHmLm5udhrUF1dnXl5ebHU1NRat/H8+XNmbGzM7dvJyYkJBAIpRC8bH0usiEQidvPmTebh4cHq1asn8d41NDRkCxYsYAkJCTxFLx7r7Nmzudi0tbXZ33//zXdYHKFQyMLDw5mdnZ3E86ihocHc3NxYXFxctXsQKSppnY/a/P+oSmLlw4cPbOTIkWL7tLOzk8rfAkIIIYSQilBihbA3b96wL7/8UuwDaGFhocR2ijLUpzICgYB98803XDzOzs689yh48+YNc3R0FHue/ve//7HExERe46oLRCIRO378OGvbtq3Y86uiosJcXFyklhh4+/Yta9OmDbd/W1tbhR/KUdGFfE5ODtu7dy/r0qVLhRezffr0YQcPHqzwvc+H4uJisZ4RKioq7MiRI3yHxRhjLC8vj/3yyy+sdevWEs+jvr4+W7JkCXv9+jW3fV1IrNT2fEjr/8enEiv3798X6xkIgC1evJiVlJTU6LgJIYQQQqqCEiufuZycHNa1a1fuA6iVlZXYkAlFHOpTmRUrVoh94/nu3TveYhEIBMzf3581adJE7Llyc3NTmKFJyuzSpUuse/fuEq9FBwcHdu/ePam1k5+fz3r06MHtv02bNuzt27dS27+slL+QHzx4MPP09GQNGzaUeL50dXXZrFmz2KNHj/gOWUxqairr06eP2EX8r7/+yndYLDU1lS1dulRiuBkAZmlpyXbv3l3h+1vZEys1PR+y+P/xscRKUFCQWC8sXV1ddubMmRodMyGEEEJIdVBi5TNWUlLCBg8ezH0INTMzY8nJyYwxxR3qU5kjR45wsamqqvI2jl4kErGLFy+yzp07SwyvUIRhScouJiaG2dvbS7webW1tpX7OBQKBWG8jExMTpelp9ODBgwrft2U/3bt3Z7/++qvCJflEIhE7evSo2LBETU1N3nuq3L9/n3l4eDBNTU2J59LOzo6dOXPmo70slDWxUtPzIcv/HxUlVgoKCtjUqVPF2ujSpQt79uxZjY6bEEIIIaS6KLHymRKJRGzSpEli3+zFxsYq9FCfyty+fVvsW0o+ZmopKSlhJ0+eZF9//bXE8zZ69GiWlpYm95jqkidPnrDRo0dLPLdWVlYsPDxc6kO+RCIRmzFjBtdOgwYN2N27d6Xahiz8+++/bO7cuUxXV1fiudLR0WFTp05lsbGxfIdZoTt37kgkzZo2bcpu3LjBSzwikYhFRkaKzTBW9qOurs5cXFxYTExMlfaljImV6p4PeQ0V/W9i5fnz58za2lqsrSlTprCCgoIat0EIIYQQUl2UWPlM/fTTT2IXCcOHD1f4oT4VSUxMZKampmJDbeRVV0UoFLK///6bLVy4UCyGsh9ra2uagaKWXr16xaZOnSpxodayZUsWEhIiswKy69evF3t/XLhwQSbtSENRURE7fPgw69u3b4Xv38aNG7Pdu3cr5PtXIBCwCxcusCFDhkjE7ejoyNLT0+UeU0FBAdu/f3+FvS10dXXZggULuJ59VaUsiZXqng8+hoqWT6xs375drF1tbW0WGBgolXYIIYQQQqpDHeSz4+/vj5UrV3L3BQIBTp8+LbaNubk53NzcMGHCBFhaWso7xCpJTU2FtbU1srKyAACWlpZYuXIl0tLSwEqThmI/ACpcXtV1BQUFePHiBZ4+fYrbt2/j+vXrSE9Pl4jLysoKixYtwtixY6GqqiqnZ6NueffuHTZs2ICff/4ZhYWF3HIjIyMsW7YMU6dOhaampkzaDgkJweLFi7n7v/76K7799luZtFUbiYmJ8Pf3x4EDByReh5qamiguLgYADB48GJ6ennyEWKHMzEzcuHEDUVFROHXqFFJSUsTWN2/eHNu2bYOTkxNUVFTkFldGRgZ2796NXbt2ISMjQ2ydhYUF5syZAw8PDzRo0EBuMclDTc5HamoqQkNDERgYiMePH0vsU17/P+bMmcPdbtWqFY4fP45OnTrJrD1CCCGEkMpQYuUzUlRUhBUrVmDDhg0Vrq9Xrx5GjhwJd3d39O3bV6GTAowxNG3aVGxZfHw8WrZsyUs8qqqqsLKygqOjI1xdXfHll18q9PNXXkpKCrp16wYPDw+sXbuW11jy8vKwY8cObNq0CR8+fOCWN2rUCD/++CPmzJkj0wvb6OhoTJw4kbu/bt06jB8/XmbtVZdAIEBERAT27NmDqKgoLvFXpnXr1pg+fTp69+6Nbt26AQBu376NH374Qe6xfvjwAaGhoWjTpg26dOmC1NRUJCQkSFy4lzE3N8f8+fMxbdo0aGlpyS3Of/75B9u2bUNwcDCKiorE1tna2sLb2xvDhw+HmpqaVNq7deuWUp6PoqIihIeHIzAwEFFRURAKhWLb8/n/w8nJCQEBAdDV1ZVbm4QQQgghYuTbQUY+3NzcuK7BxsbGNd7PmDFjxLo0K+N0jeW7ajdq1EjphvpU5unTpxUei6L86Ovrs6FDh7JffvmFpaam8v10fVT5uMeOHctLbYKioiK2a9cuZmxsLBaPlpYWmzdvHsvIyJB5DHfv3hWbOcfT05P36brLvHr1iq1cuZKZmZlVWO9j9OjR7NKlS1y8CQkJvL8HqvKjoaHBhgwZwo4dO8aKi4vl9nyWFZkeNGiQREyqqqps9OjR7O+//5Zae8p6PhRxVjhXV1eubTU1NbZlyxaFeZ8SQggh5POlNImVskKSFy9elFj37NkzVr9+fWZnZ8dEIhFzc3NjhoaGLCQkhB07dkxs219//ZX169ePmZiYME1NTWZqasoGDhzIrly5IrHfa9eusZCQENa7d28GKFdi5VOzMtSvX58tWbJEYWb1qa7yNQsU/UdNTY05ODiwqKgohbwA0NDQEIvX2tqaPX/+XC5tC4VCFhYWxiwsLCQubidNmsSSkpLkEkdiYiIzMTHh2nd0dJRZ/ZaqEgqF7Pz588zJyanCYqAtW7Zk69atq7AwslAoZP/73/94f+3/98fAwID16tWLeXt7sxMnTrDs7Gy5PqdFRUUsMDCQderUSSK2hg0bMm9vb5nM/KRs50ORZ4U7fPgwU1VVZc2aNaMaVoQQQghRGCqM/acvuYLKycmBlZUV1NTU8ODBA+jo6AAAGGPo378//v77bzx48ABffvkl3N3dceXKFbx48UJiPzNnzsT79+/RsWNHGBoaIiMjA6GhoXj06BGOHDkCZ2dnice4u7sjKCgIJSUlUFdX3NFTn+qqXaZz5864ceMG6tWrJ+cIpSchIYEbuz9w4ECsXr2alzgYYygpKUFOTg7S0tKQkJCAuLg43LhxA2/fvpXYvkuXLli3bh0GDhzIQ7QVc3V1RVhYmNgyPT09hISEwMHBQSZtMsYQFRWFxYsXIy4uTmzdyJEjsXr1arRr104mbf/Xu3fvYGtri3///RcA0KNHD/z++++8vT8yMjIQEBCAvXv34vnz52LrVFVVMWTIEEyfPh329vYfHZ4iFApx//79Sv8OyENGRgZMTU3RsGFDGBsb81afJDMzE3v37sXOnTuRmpoqtq558+aYPXs2Jk2aJNOhJIp+PhR5qM9/paWlwdDQUKH/HxNCCCHkM8NrWqeaIiIiGAA2e/ZsbtmePXsYALZlyxZumZubG2vRokWV95ubm8uMjY3Z119/XeH6sqFFithjpSpdtRs0aMDdtrKyYllZWXyHXWuKPsuGUChkMTExzMfHh5mbm0uck6FDh7KXL1/yHSZjTHyWjf/++Pj4SL3nxl9//cX69Okj0Va/fv3YzZs3pdrWp+Tn5zNbW1suhtatW7O3b9/KNQbGSt/Hf/zxBxs7dqxEDyIAzNTUlC1fvlxuPXjqiqdPn7IZM2aITcde9tO9e3d2+PBhhfy7Li+KONSHEEIIIUQZKVVihTHGxo8fz1RVVdn169dZcnIya9SoEevWrZvYxV91EyuMMdahQwfWtm3bCtcpYmKlKl21fXx82DfffMMtMzMzq/Y0oYpK0RMr5QkEAnb8+HFmbW0tdo4aNWrEwsLC+A5PLLESExPDnJycJBIeFQ03qa4HDx6wYcOGSbxWbWxsWHR0tBSOpHoEAgEbMWIEF4exsbHchkCVeffuHduxYwdr165dhe9je3t7duLECbnWH1F2IpGIXblyhQ0bNoypqKiIPZ8qKipsxIgR7M8//1TIYXnyoshDfQghhBBClJHSJVYyMzOZkZERa9euHRs4cCDT0NBg9+/fF9umKomVd+/esfT0dPbo0SM2f/58BoDNmTOnwm0VJbFSWFjIjh49yhwcHCqsuVCvXj3m6urKLl68yAQCAZs0aRK3TldXlz148IDX+KVJmRIrZYRCITt48CBr2rSp2HmbNWsWr6+t8omV+Ph4JhKJ2JYtW8ReY02bNmXXrl2r0f4TExPZhAkTJC5yW7duzY4ePcrLBa5IJGI//PCDWK+u2NhYubV98+ZN5uHhUWFPCkNDQ7ZgwQKWkJAgl3jqiuLiYhYWFsZsbGwknlMdHR02c+bMz/o5rc7/D6FQyHe4hBBCCCFKRekSK4yVFq8r+zD4008/SayvSmKlRYsWYh8oPT09K50Nhc/ESk27av/000/cek1NTXb58mW5xy5LyphYKfP+/Xs2fvx4sXM4fPhwXmbjYUwysVLmjz/+ECvoqqamxnx9faucCElLS2MzZ86UGNrSrFkz5u/vz2syaePGjVw86urqLCoqSuZt5uTksL1797IuXbpU+D7u06cPO3jwICssLJR5LHVJVlYW27RpU4UzJjVr1oxt3LiRvXv3ju8weUFDfQghhBBC5EMpK78ZGhpytwcNGlSjfYSFhSEvLw8vX75ESEgIcnJyUFBQAG1tbWmFWSupqakIDQ1FYGAgHj9+LLHe3Nwcbm5umDBhAlfEtYy/vz9WrlzJ3Q8JCYGdnZ2sQyZVpKuri+DgYPTu3RteXl4oKSnB6dOnMXLkSJw4cQJaWlp8hwgA6NOnD+7evYuxY8fiypUrEAqF8Pb2xl9//YVff/0VjRo1qvBx2dnZ2LJlC3x9fZGXl8ct19PTg4+PD7y8vHgtnBwWFoaFCxdy9/fv34/vvvtOZu3dv38fe/bsQWhoKHJycsTW6erqws3NDdOmTUP79u1lFkNd9Pz5c+zYsQMHDhwQe50BpUWi582bh9GjR0NDQ4OnCPlTm/8fhBBCCCGkBvjO7FRXXl4es7CwYObm5kxPT49ZW1tLFNesbo2VkpISZmNjw3r16lXhenn1WJFGV+3w8HCxx/r6+so0Zr4oc4+V8qKjo5mOjg53LGPHjpX70JjKeqyUKSkpYYsWLRJ7LVpaWkoMwSsoKGBbt25lBgYGYtuWTe2tCEWTL168KNaDZs2aNTJpJz8/nwUFBbEePXpU2Euge/fu7Ndff2V5eXkyab+uEolE7K+//mIjR45kqqqqEs/r0KFD2ZUrVz7L+ik01IcQQgghhD9Kl1iZO3cuA8AiIyPZgQMHGAC2ceNGsW1qUrx2w4YNDECFxfpkmViRZlftmzdvsvr163OP8/b2lnq8iqKuJFYYKx1yU77Whqwu9ivzqcRKmdOnTzNdXV2xC7WgoCBWUlLCDhw4IDH7kbq6OvPy8mKpqalyPJrK3bt3jzVs2JCLb9q0aVK/AP/333/Z3LlzK3wv6+josKlTp8qtlktdUlJSwg4fPsy++uqrChMGnp6e7MmTJ3yHKXc01IcQQgghRDEoVWLl77//ZqqqqmzChAncsv79+7N69eqJXRDWJLFSVpOkouleZZFYkfasDPHx8czQ0JB7/JgxY+r0t5J1KbHCGGOnTp3iiruqqqqyK1euyK3tqiZWGGPs2bNnEjVCGjduLHZfRUWFubi4KFSh0BcvXjBTU1MuxmHDhknt/VxUVMQOHz7M+vbtW+F7uWPHjmz37t10YVsDHz58YL6+vmI1scp+TExM2Jo1a1hGRgbfYcodzepDCCGEEKJYlCaxUlRUxNq3b8+MjY1ZZmYmt/zZs2esfv36rG/fvtyyyhIrJSUlYo8t8+HDB9aqVSumo6PDcnNzJdZLK7Eiq67ab968YV9++SW3Hzs7O4UvgCkSiWrVW6CuJVYYY2zVqlXcMVlYWFT4WpSF6iRWGCsd8jN48OAKL+gcHBzYvXv35BB11WVmZopNZ/z1119LZQjO8+fP2eLFi5mRkZHE86ClpcUmTJjArl+//lkOS6mtly9fsnnz5rFGjRpVmKgKDAxU+L9x0kZDfQghhBBCFJfSFK9ds2YNHj9+jCNHjkBfX59bbmFhgVWrVmH+/PnYv38/Jk+eXOk+cnNzYW5uDmdnZ3To0AH6+vp48eIFAgMDkZKSgl9++QU6OjpSjZsxhpiYGAQGBuLQoUPIysqS2KZXr15wd3fHqFGjKi0IWpnc3Fw4ODjg2bNnAAArKyucPHlSYQqg/ldubi5WrFiB3bt3Q1VVFY0bN67RfgQCAXc7KSlJStHxy8fHB9HR0bh27RqeP3+OtWvXYt26dXyHJSY2NhY+Pj64cOGCxLoGDRrA09MTnTt35iGyihUWFsLR0RH//PMPAMDS0hLh4eGoX79+jfYnEAgQERGBPXv2ICoqCowxsfWtW7fG9OnT4ebmJvZ3ilTN7du3sXXrVhw7dgxCoVBs3aBBg+Dt7Y3+/ftDRUWFpwjlS9b/PwghhBBCiJTwnNipkri4OKahocEcHR0rXC8QCFjXrl1Z48aN2evXryvtsVJUVMTmzp3LunTpwho3bszU1dWZkZERGzp0KLt48WKl7dekx4o8umqXlJSI9RwwMzNjycnJNd6frIWHh7PmzZtX+HzU5sfAwIDvQ5Oap0+fMk1NTa7Xw8uXL2XeZlV6rDx58oSNHj1a4rlv1aqV2BAbAMzHx0eioDQfBAIBc3Z25uIyMjJiz549q9G+Xr16xVauXFnhlL7q6ups9OjR7NKlS9Q7pQYEAgE7ceIE69WrV4U9fyZPnswePnzId5hyRUN9CCGEEEKUi1IkVqrLzc2NmZubs4yMjAqH/lRVdnY2y8jIYN9//32VEivy7KotEonYpEmTuH3r6uqyBw8e1GqfsvLq1Ss2cuRIsedCQ0ODmZiYsGbNmtXox9jYmNtX7969+T5Eqfrxxx+5Y/Py8pJ5ex9LrLx69YpNnTpV4vXcsmVLFhISwgQCAXv//j1zcnISW9+vXz+WlpYm89grIxKJ2KxZs7h4dHR0WExMTLX2IRQK2fnz55mTk1OF7+eWLVuydevW8XqcyiwnJ4f9/PPPYsMYy36aNGnCVqxYwd68ecN3mHJDQ30IIYQQQpRXnU2slH0YNTY2rvF+xowZI/bBtqLECl+zMpQV2wXANDU12eXLl6W2b2kRCATs559/FpuJBQAbMGBAlWp5fExdrLFS5u3bt9wUzNra2rVKDlZFRYmVzMxM9uOPPzJtbW2xc2dkZMR+/vlnVlRUJLYPkUjEtmzZInZB2LRpU3bt2jWZxl6ZzZs3c3GoqamxiIiIKj82PT2dbdy4kVlYWEi8l1VVVdmwYcNYRESEQvTKUUbJycls4cKFEkWPAbB27doxf39/lp+fz3eYckGz+hBCCCGE1A11MrHy6NEjFh0dzaKjo9nVq1drvJ8HDx5w+4mOjhbr5s9nV+19+/aJtXX48GGpt1Fbd+/eZd26dZP4Fjo0NFQqwyXqcmKFMSbW22L79u0ybat8YiUuLo6tXbtWbFplAKxRo0Zs9erVLCcn56P7unr1qtjQIDU1Nebr6yvXITIHDx4Ui/3XX3/95GNEIhH7448/2NixY5mGhobE+9nU1JQtX76cJSUlyeEI6qY7d+4wV1dXpq6uLvH8DhgwgEVERHw2PTFoqA8hhBBCSN1SJxMrsqIIXbXDw8PF2vb19ZVJOzWVk5PD5s2bJ/H8TJ48Wao9L+p6YuXhw4fc8X311Vcybat8YqX8lN1AaY2LefPmVWtK29TUVGZnZye2n5EjR8rlG/fff/9dLDGyatWqj27/7t07tmPHDrFZg8r/2NvbsxMnTrDi4mKZx14XCYVCFh4eLvF6AEqHA7q5ubG4uDi+w5QLRfj/QQghhBBCZIMSK5+gSF21b968yerXr8+16+3tLdP2qqui4rTt2rWrVa+hytT1xApjjHXq1Ik7xlevXsmkDaFQyHr27FnhkJdJkybVuIdGSUkJW7Rokdg+LS0t2f3796v0+Ly8PBYYGMgWLlzI5syZw1atWvXJx8bFxYlNzztlypQKe8qIRCJ28+ZN5uHhwerVqydx7IaGhmzBggUsISGhRsdOSs/fL7/8wlq3bi3x/Orr67MlS5aw169f8x2mzCnS/w9CCCGEECI7lFiphKJ11Y6PjxfrTTBmzBiF+VazouK0WlpabM2aNRK1OKTlc0isLF26lDvG4OBgqe5bJBKxiIgI1rlzZ4nX9siRI9njx4+l0s7p06fFhhXVq1ePBQUFVbp9bm4umz9/fqUXob1792a///67xONevnzJmjZtym03ZMgQiZpIOTk5bO/evaxLly4V7rtPnz7s4MGDrLCwUCrH/jlKTU1lS5cuZQYGBhLPr6WlJdu9ezfLy8vjO0yZU7T/H4QQQgghRLY+i8TKw4cP2alTp9j58+dZbm5updspalftN2/eiM2cYWdnpxAXf7IsTvspn0Ni5dKlS9wxzpgxQ2r7/euvv1ifPn0qvOA7duyY1Nop8+zZM4lkxtSpU1lBQYHYdu/evWNdu3atMK7yP2pqaiwgIEDsceUvYLt37y72Po+Li2Oenp4Sr1OgdDatWbNmsUePHkn9uD8n9+/fZx4eHtxU4eV/7Ozs2JkzZxQmESwrivr/gxBCCCGEyF6dTqzcunVLYpiDrq4uW7x4MfdttqJ31c7JyRG72LSysmJZWVlyj+O/ZF2c9lM+h8TKhw8fuGP8+uuva72/Bw8esGHDhlU4NKPstqwSYgUFBWzKlCli7VpbW7Pnz58zxkqTdN988w23TkNDg02YMIGdO3eO/fXXX2z79u2sTZs23HpVVVV2/vx5VlBQIJYkatWqFUtPT2f5+fksKCiI9ejRo8L3dPfu3dmvv/76WfSekBWRSMQiIyPZt99+K/H8qqurMxcXl2pPca1sFP3/ByGEEEIIkY86m1j5bz2S//4MHTqUbdiwQaG7apeUlLDBgwdzMZmZmbHk5GTe4mFMfsVpP+VzSKwwxpiZmRkDSut+1FRiYiKbMGECU1FRETtnrVu3ZkePHmXjxo2TeWKlTEBAgNgUznp6euzs2bPs7Nmz3DIjI6MK66kIBALm5eXFbde1a1c2atQoscTehQsX2Ny5cyu8yNXR0WFTp05lsbGxMj3Guq6goIDt37+/wr+durq6bMGCBbz/nZI1GupDCCGEEELKq5OJFZFIxP73v/99ckiBInfVFolEbNKkSWIXLA8ePOA1JnkWp/2UzyWxYmtryx3nf4fOfEpaWhqbOXOmxPTBzZo1Y/7+/lyvrfKzAsk6scIYY/fu3WOtWrUSi6n8ULcTJ05U+lihUFhhXRhNTU1mY2NT4fu6Y8eObPfu3dRjoJbS09PZihUrWJMmTSSeYwsLC+bn5/fJ6biVGQ31IYQQQgghlVFHHRQTE4N79+5VeftevXrB3d0do0aNQqNGjWQXWDWsXLkSBw4cAABoamri1KlTsLKy4iWWlJQUzJ49G8ePH+eWaWlpYdmyZfjxxx+hqanJS1yfAwMDA+52VlYWTE1NP/mY7OxsbNmyBb6+vsjLy+OW6+npwcfHB15eXqhXr55M4q2Kzp07IyYmBh4eHjh58iQA4NmzZwCAZs2aYdj/a+/Oo6K6sraBP0wSQCXSoBJFWWpIa8C00iF2HBojy4SgnYjGMhIFUaAQjVCor0NsEYOaRApwLMRqERyIGvFFGzGxxYhxAI0DRuOEEzjhCMhY1v3+4LPe3C5QQIqC8vmt5VrW2feeuwvIUJuzz/nHP2q919jYGCEhIQgMDBSNV1ZW4vjx45rX5ubmkEgkkEql6NevH4yMjHTwTl4N586dQ0xMDJKSklBRUSGK9e/fHzKZDJ988glMTEz0lKHuCIKAY8eOITExEZs3b8bDhw+1rmmO//0gIiIioqZlkIWVs2fP1vnaTp06wdTUFAcPHkR+fj4cHR01f57FmlpCQgIWLFigeZ2cnAx3d/cmz+Pp06dYvXo15syZg+LiYs24h4cHVq9ejR49ejR5Tq+aPxZA+vbt+9wPr4IgoKSkBCUlJVCr1ZpxIyMjmJubo6SkBIsXL0ZsbKzovgcPHmj+vnv3bkydOrXx3kAtrK2t8cMPP2Dx4sWYO3euZrxNmzbPfY8qlQpFRUW1xp2cnCCVSuHr6wsbG5tGzflVIggC9u3bh+joaOzevVsUMzY2xqhRoyCTyfDee+/pKUPdunXrFjZs2IDExMQa/3vi4OAAX19fjB8/Hm+++aYeMiQiIiKi5sQgCyvm5uZ1vragoAAFBQU1xkxMTODg4CAqtui68LJr1y4EBwdrXsvlcowePbpRn1EXJ0+eRGBgIHJycjRjdnZ2iImJwdixY7kCoIkIgqD5++3btxs8R3l5OQBxEaUma9eubZLCCgBcvXpVtAoKAMzMzGq8tqCgAEqlEgkJCcjPzxfFTE1N4e3tDalUCnd3d/5svoTKykps3rwZcrkcp0+fFsXatGmDgIAATJ06FY6OjvpJUIcqKiqwc+dOJCYmIiMjA0+fPhXFLSwsMHLkSPj5+WHw4MEwNjbWU6ZERERE1NwYZGFl8ODBMDMzQ1VV1XOvs7Ozg0qlqnF5N1C9YuPq1au4evVqjfHGLrxkZ2dDIpFo/odeJpMhLCyszvc3hpKSEkRERCA2Nlb0wWLSpEn45ptvuAqgif1xdYa9vb3ow9yzgklRURFUKpXoPgsLC7Rt21bz81dWVoaSkhK0bt1aqw3owYMHKCsrA1D9fW4K//73v/HFF1/g0aNHovELFy7g/v37+NOf/gS1Wo29e/dCoVAgLS1N64MuAHh6emLdunXo0KFDk+RtqO7fv4/4+HisWLECt27dEsW6dOmCadOmYeLEibC2ttZThrrBVh8iIiIiagwGWVjp0KEDfHx8kJiYWOs1rVq1wsGDB+Hk5ITHjx/j2rVrmiLKf/9pisLLpUuX4OXlhdLSUgCARCLBd99991Jfh/ratWsXQkJCcP36dc1Yz549ER8fj4EDBzZpLlTt2SoVExMT3LhxQ9Mmk5mZiVmzZiE7O1t0vZeXF6KiovDOO+/U+RlffPEFNm7cCKC6UKFLT58+xT//+U8sWrRIM9ajRw/069cPGzZsQEVFBf75z3+ia9euiI+PR15enuh+Y2NjGBsbQ6VSwczMDOvXr4ednZ1OczZkFy9eRGxsLNatW6cprj3j5uaG8PBweHt766UlUpfY6kNEREREjcmw/m/5D5YvX47Lly8jKytLK2ZmZoaNGzfCyckJQPV+D71790bv3r1rnEvXhZc33ngDubm5mn1M/vKXvyAyMhJqtbpJlptzc9rmSRAEXLlyBUD1qgETExMcP34cc+bMwY8//ii6tn///li8eHGzLoDduXMHY8eOxb59+zRjI0aMwLp163Dnzh1s2LABALBq1Sqte+3t7fHRRx8hMzNT88/TmDFjWFRpAEEQcODAAcjlcuzcuVPUbmZkZIQRI0ZAJpPh/fffN6i2Krb6EBEREZGuGGxhpXXr1vjpp5+QnJyMNWvW4OLFi7CwsMDw4cMxderUep2w09SFl5MnT+Ktt97S+R4v3Jy2ebt+/ToeP34MoPo36BKJBFu2bBFd4+zsjMWLF8PLy6tZfwg+ePAgJBIJbt68CaC6qPjNN99gwoQJWL9+PRQKRY33dejQAS4uLrh79y7WrVunGe/WrRuWLl3aJLkbiqqqKmzduhVyuVx0ghIAWFlZwd/fH9OmTUP37t31lGHjY6sPERERETUFgy2sANWrLiZNmqTzfSMaWni5cuUKzpw5o7U/xjO63OOFm9M2f4cOHdL8PSsrS7SywNHREQsXLsTnn3/erI+5FQQBMTExmDlzpmaFQMeOHREREYGjR4+ic+fOWi0of3Tnzh3cuXNHNNarVy+kp6ejffv2Os3dUDx69AgJCQlYtmyZ1sa/nTp1wpdffomAgAC0a9dOTxk2Prb6EBEREVFTMujCSnNRU+FFEAQEBATg5MmTAKpP3IiKioIgCDrd46Vjx47Yt28ftm3bJjqSl5vTNi8PHjwQ7UPyrKjSvn17zJs3D4GBgc2+RauoqAj+/v6iFjMnJye0atUKUqlU6/pBgwZBKpXCyckJSqUSycnJKCkp0cRdXV0REhKCMWPGaG3AS9ry8vIQFxcHpVKJJ0+eiGJ9+vRBeHg4Ro8eXetJTC0NW32IiIiISF9YWNGTBQsWQKlUAqjeSDctLQ3u7u41XqurPV6A6v1mnJ2doVKpsHz5cp0fJ03P9+TJE8TFxeHbb7/VtAEBQNu2bTFjxgyEhoaidevWesywbnJzczFy5EhcvHhRM9aqVStcuHBBdJ21tTV8fX0RFBSEXr16acZdXV3x3XffIT8/H+Xl5bCxsYGDg0OT5d9SCYKAw4cPQy6XIzU1VVQ8BYDhw4cjPDwcgwYNMohVaWz1ISIiIqLmgJ+a9SAhIQELFizQvE5OTq61qALobo8XoHrfhRMnTuDEiRNaMV3v8UL/p7KyEmvXrkVkZKRW64uTkxN++eUX2Nra6im7+klKSkJQUBDKy8tF45WVlZq/u7m5QSqVQiKRwNLSssZ5rKys8NZbb+k0V0OhUqmwfft2yOVyHD16VBSzsLCAn58fQkNDNRt2t3Rs9SEiIiKi5oSfipvYrl27EBwcrHktl8sxevTol5qztsLLs81pZ8+eLWqp6NKlC9566y3cu3evyY6Tppqp1WqkpKRg3rx5WkcLPxMbG9siiirl5eXw9fXV2mD3GSsrK/j4+CAoKAh9+/Zt4uwMU1FREZRKJeLi4nDt2jVRrGPHjpgyZQqCgoJaxM/Pi7DVh4iIiIiaK37qbULZ2dmQSCSaDwQymQxhYWE6eVZ9NqfV9XHStRVeunTpYhDtCA0hCAIyMjIwe/ZsnDp1ShQbPHgwMjMzAVSffjN06FB9pFhnlZWVWLNmjVYB7xkXFxcEBwfDx8eHrRiN5Pr161i2bBkSEhJQVFQkirm4uCA8PBxjxoyBubm5njJsHGz1ISIiIqKWgIWVJnLp0iV4eXmhtLQUACCRSPDdd981+nNKSkoQERGB2NhY0W90n7c5bVMfJ/2MlZUVXn/99Xq/RwCik5SuX7/eoDn05dChQ5g9ezYOHDggGv/ggw+waNEi/M///I9m7H/+53+a7ak/V65cQUJCAlavXo1Hjx6JYqamphg7diykUin69ev3yhbQGltOTg6io6Oxbds2rRUbnp6ekMlkGDJkSIv/erPVh4iIiIhaEhZWmsDdu3fx0Ucf4d69ewAAd3d3rF+/vtGXqu/atQshISGiQkPPnj0RHx+PgQMHNnheXRVenjx5onVaSUPU9MGrOTpz5gzmzp2LtLQ00birqyuWLFkCDw8PbNy4ET///DMAoEePHvDz89NDprVTqVRIT0+HQqFARkaG6AhooHoz5GnTpmH27Nk8YaqRPH36FGlpaZDL5Th48KAoZm5ujnHjxiE0NBRvv/22njJsHGz1ISIiIqKWioUVHSspKYGXlxcuX74MAHB2dkZqamqjLtEvKCjAtGnTRMfampubY968eZgxY4bOj+VtSOElOzsbV65cafBv1lUqlWaT1z+eJtMcXb16FfPnz0dycrKoEOHk5ISoqCiMHDkSRkZGKCgowJdffqmJy+XyZnOkckFBAZRKJRISEpCfn1/jNQMGDMDOnTsbvAqJxEpKSpCYmIjY2FjNvz+esbOzQ0hICIKDg9G+fXs9Zfjy2OpDRERERIaAhRUdUqlUkEgkOHbsGACgc+fO2L17d6N98Hy2Oe2cOXNQXFysGffw8MDq1avRo0ePRnnOy3pR4aUhLl26pGkB6NKlS6PN25ju3LmDqKgoKBQKVFVVacY7deqEiIgI+Pn5aTb3raysxOeff44HDx4AAEaPHo3hw4frJe9n1Go19u7dC4VCgbS0NK0VBM8YGxvj22+/hUwma/EtKM1Bfn4+VqxYgfj4eK0Wq549e0Imk8HHxwcWFhb6SbARsNWHiIiIiAwJCys6IggCpFIp0tPTAVQXF3bv3o3OnTs3yvz12ZyWmlZRURGWLl0KuVwuanVq164d5syZg5CQENGH4mc/K1lZWQCqP1SuXr26yfN+prCwEOvWrUN8fLzWSUVGRkaiVTf29vb4/vvvX6rVjKqdOHECcrkcKSkpoj2EgOpiqUwmw4cffthiW2DY6kNEREREhoqFFR1ZsGABlEolAKBVq1bYsWMHnJ2dX3rehmxOS02jvLwcq1atwqJFi3D//n3NuKWlJcLCwjB9+nSt1UqCICAsLAzr1q0DALz22mvYunWr3r6PYWFh2LNnj2iFDVB9dG+7du1w7tw5zZi7uzs2b96Mjh07NnWaBkOtViM9PR3R0dHYv3+/KGZmZoaxY8dCJpM16mqvpsRWHyIiIiJ6FbCwogMJCQlYsGCB5nVycjLc3d1fel5dbU5LL0elUiEpKQkRERG4ceOGZtzU1BRBQUH46quvaiw+VFVVISgoSFNUMTIyQlJSEt57770my/3hw4f4/fffNa937dolig8dOhSenp5YuXKlqKgye/ZsREZGalqZqH5KS0uRlJSEmJgYXLhwQRSzsbFBcHAwQkJCYG9vr6cMXw5bfYiIiIjoVcJPRY1s165dCA4O1ryWy+UYPXr0S82p781pqWaCICA1NRVz584VFSeMjIwwduxYLFiwAN27d6/x3tu3b0MikWiOXDYyMoJSqcRnn33WJHnn5ORAoVAgJSUFZWVloritrS38/f0RGBiIX375BVKpVHONtbU1kpOT9b7/S0t1+/ZtrFy5EqtXrxatagKAN998E2FhYfD19YWlpaWeMmw4tvoQERER0StLoEZz9OhRwdLSUgAgABBkMtlLzadSqYTly5cLbdq00cwJQPDw8BAuXrzYSFm3TBcvXtR8PXx8fJr8+fv27RPc3NxE3xcAgpeXl3Dy5Mla71Or1cLWrVsFW1tbzT2tWrUStmzZovOci4uLhfj4eKFPnz5aeT/7I5fLhfLycqGsrEwIDAwUxfr06SNcvnxZ53kaotOnTwsTJkwQWrVqpfU1d3d3F9LS0oSnT5/qO816U6vVQnZ2tjB58mShXbt2Nf5MDRgwQFi7dq3w+PFjfadLRERERKQTXLHSSC5dugQvLy+UlpYCACQSCb777rsGz8fNaZun48ePY86cOfjxxx9F4/3798fixYuf25J14sQJzJo1S3TvG2+8gR9++AH9+vXTWc6nT5+GQqHAhg0bRKdHAdUrUDp27Ijz588DAIYPH46bN29i1KhR+PXXXzXXBQQEYNmyZXjttdd0lqehEQQBe/bsgVwux08//SSKmZqaQiKRICwsDK6urnrKsOHY6kNERERE9Af6ruwYgjt37gjdu3cX/Qa6vLy8QXMVFxcL4eHhgomJiei3vpMmTRLu37/fyJm3XE29YuX8+fPC6NGjtX4b7+zsLOzcuVNQq9U13qdSqYQff/xRGDZsmNa9n376qXD37l2d5FtaWiqsX79e+Nvf/lbjKgI3NzfhX//6l/DkyRPBx8dHMx4bGytaefDaa68JiYmJOsnRUJWVlQlr164VevXqpfV1t7a2FmbOnCncuHFD32nWW3l5ubB161bBy8tL699PAAQLCwvhiy++EPbu3dsiV98QERERETUUV6y8pJKSEnh5eeHy5csAAGdnZ6SmpsLc3Lzec3Fz2uanoKAAkZGRUCqVoj0jHB0dsXDhQnz++ecwMTER3XP//n0cPnwYGRkZ2LFjBwoKCkTxLl26ICYmBiNGjGj0lUfnz59HfHw8EhMTtU5gsbKygo+PD4KCgtC3b98a7w8NDdX8vUePHvjhhx9a7Ik0Ta2wsBCrVq3CypUrUVhYKIp169YNoaGhmDBhAlq3bq2nDOtP4Kk+REREREQvxMLKS1CpVJBIJDh27BgAoHPnzti9e7fWkbovws1pX052djamTJnSqHOWl5fj119/xenTp0UFFQsLC/z1r3/F22+/jT179mDcuHF466230KdPH9y6dQuXLl3SKqQ84+DggOnTpyMoKKhBhbfaVFZWYseOHVAoFMjMzNSKu7i4IDg4GD4+PnX+4DtixAisW7cO1tbWjZanoTp37hxiYmKQlJSEiooKUax///6QyWT45JNPtApwzRlbfYiIiIiI6kHfS2Z0wdfXV7M8vUOHDg2eRyKRiJa6V1VVaWJqtVqYOHGiaIl/bm5uvebn5rQNd+nSpVo3YG1Of8zMzIRhw4YJ27ZtEyorKxv1a5CXlyfMnj1baN++vdZzzc3NhfHjxwuHDh2qtU3pmS+++EJzn4mJibB06dIX3vOqU6vVwt69ewVPT0+tr72xsbEwevRo4ciRI/pOs17Y6kNERERE1DAtprAyefJkAYCwd+9erdjly5cFS0tLwd3dXVCr1YKvr69ga2srJCcnC9u2bdNc9/TpU2H9+vWCt7e34OjoKFhYWAg9evQQAgMDhYKCAq15s7KyhOTkZGHgwIFahZX58+eLTnXJzMys1/s5ceKE8O6774o+uNjZ2QkbNmzgh9o6ePr0qfCXv/xF74WT//7zpz/9SRgwYIAgk8mE7du3C0VFRY36vquqqoT//d//FTw9PQUjIyOt5zs5OQlyubxe+/F8//33grGxsdCpUyfhwIEDjZqvoamoqBASExOF3r17a33t27RpI8hkMuHKlSv6TrPOeKoPEREREdHLMxIEQUALUFxcDGdnZ5iYmCA3NxdWVlYAqvcAGDJkCI4cOYLc3Fx0794dfn5+2L9/P65evSqao6SkBG3atEHfvn0xfPhwODg44Pfff8fq1athaWmJY8eOoUuXLlrP9vPzw/r161FVVQVTU1MkJCQgMDBQE//+++8xevToOr2PkpISREREIDY2VtRiMmnSJHzzzTewsbFpwFfn1fT06VOtVp36UqvV+PHHH6FQKEQtPMbGxhg+fDgmTZqEjh071np/YWEh7O3t0aZNG3To0EFn+2cUFBRAqVQiISEB+fn5opipqSm8vb0hlUrh7u7eoH1bbt++DVtbW5iasjuwJvfv30d8fDxWrFiBW7duiWJdunTBtGnTMHHixBbTOsVWHyIiIiKiRqTnwk69pKenCwCEadOmacYUCoUAQFi6dKlmzNfXV+jatavW/RUVFTX+Rv4///mPAECYOnVqjc991lpUVVUl7Ny5U7RMXi6X1zn/nTt3Cl26dBH9Nrhnz55cJaAHarVaSE9PF9555x2t39CPHDlSOHv2rL5TFJ4+fSrs2bNHGDFiRI2tGY6OjsKiRYuE27dv6ztVg3XhwgVh8uTJgoWFhdbX383NTfj+++9FK9maM7b6EBERERHpRosqrAiCIIwbN04wNjYWDh06JNy4cUNo27at8O677woqlUpzTW2FleexsbERPvjggxpjzworv/zyi2Bpaan5ICKTyeo0d35+vjBy5EitPTC+/vproaKiol550sv75ZdfhEGDBml9sPzggw+Eo0eP6js94e7du8I333wjdOvWrcb9O/7xj38I6enpop95ajxqtVrYv3+/8I9//EOr3crIyEjw9vYWDh482CJa9tjqQ0RERESkey1u3X9sbCz27NmDiRMnomvXrigrK4NSqXypEzeKi4tRUlKC9u3bP/e6f/zjHygtLQUASCQSfPfdd8+9/unTp1i9ejXmzJmD4uJizbiHhwdWr16NHj16NDhnqr8zZ85g7ty5SEtLE427urpiyZIl8PDw0FNm1S1tWVlZUCgU2LZtG6qqqkRxe3t7BAQEYNKkSXBwcNBTloatqqoKW7duhVwux/Hjx0UxKysr+Pv7Y9q0aejevbueMqw7tvoQERERETWdFldYsbGxwfLlyyGRSHDu3DnMnz8fLi4uLzXnd999h8rKSowdO7bGeHl5OYDqfRYAwN3dHevXr4exsXGtc548eRKBgYHIycnRjNnZ2SEmJgZjx45t0D4Y1DBXr17F/PnzkZycDOEPWwo5OTkhKioKI0eO1Nv34+HDh0hOToZCocC5c+e04kOHDoVUKsWwYcNgZmamhwwN36NHj5CQkIBly5Zp7V/TqVMnfPnllwgICEC7du30lGHdVFRUYOfOnUhMTERGRobW3kMWFhYYOXIk/Pz8MHjw4Of++4uIiIiIiOquxRVWAMDW1lbzd09Pz5eaa/fu3YiKioK3tzeGDx+uFS8pKcHevXs1r52dnZGamgpzc/Ma5+PmtM3HnTt3EBUVBYVCIVoB0qlTJ0RERMDPz08vm7UKgoCcnBwoFAqkpKSgrKxMFLe1tYW/vz8CAwNbxOqIliovLw9xcXFQKpV48uSJKNanTx+Eh4dj9OjRzbqgJQgCjh07hsTERGzevBkPHz7UumbAgAHw8/PDZ599hrZt2+ohSyIiIiIiw9biCiulpaUICAiAg4MDSkpKMHnyZGRnZzeoFejIkSMYPXo0XF1dsX79eq24SqWCRCLRrFTp1KkTdu/ejddff73G+Xbt2oWQkBBcv35dM9azZ0/Ex8dj4MCB9c6PGqaoqAhLly6FXC4XfWBu164d5syZg5CQEFhYWDR5XiUlJdi0aRMUCgVOnDihFR80aBCkUim8vb1rLdzRyxEEAYcPH4ZcLkdqairUarUoPnz4cISHh2PQoEHNelUZW32IiIiIiJqPFldY+eqrr5CXl4fdu3fj5s2bmDhxIqKjozFz5sx6zXPy5El8/PHH6Nq1KzIyMrSOyRUEAVKpFOnp6ZqxXbt2oXPnzlpzFRQUYNq0afjhhx80Y+bm5pg3bx5mzJiBVq1a1fNdUkOUl5dj1apVWLRokaYYBgCWlpYICwvD9OnTay2K6dLp06ehUCiwYcMG0V47AGBtbQ1fX18EBQWhV69eTZ7bq0KlUmH79u2Qy+U4evSoKGZhYQE/Pz+EhobCyclJTxm+GFt9iIiIiIiaKX3unFtfR44cEYyNjYXx48drxoYMGSJYWFgIFy9e1Iy96FSg3377TbC1tRW6d+8u3Lx5s8Zr5s+fLzqJBf//uOU/UqlUwvLly4U2bdqITtnw8PAQ5UO6VVVVJSiVSsHBwUH0fTA1NRVCQkKEW7duNXlOpaWlwvr164W//e1vNZ7E4ubmJvzrX/8Snjx50uS5vUoeP34syOVyoWvXrlrfg44dOwpff/21UFhYqO80a8VTfYiIiIiImj8jQfjDbp7NWGVlJfr06YP79+/j7Nmzmr1K8vLy4OLigvfeew/79u0DAPj5+WH//v24evWq1jyXLl3CoEGDYGJigqysLDg6Ompdk5CQgMDAQM3rv//97/j5559RVVWl2ZODm9PqnyAISE1Nxdy5c/H7779rxo2MjDB27FgsWLCgyfcoOX/+POLj45GYmKi134WVlRV8fHwQFBSEvn37Nmler5rr169j2bJlSEhIQFFRkSjm4uKC8PBwjBkzptm2XLHVh4iIiIio5WgxrUBff/01zp49iy1btog2gO3WrRsiIyMxffp0rF27FpMmTap1juLiYnh4eODWrVuYO3cuDh48iIMHD2rirVu3hqmpKYKDgzVjcrkcp06dws8//wyAm9M2F5mZmZg1axays7NF415eXoiKisI777zTZLlUVlZix44dUCgUyMzM1Iq7uLggODgYPj4+3DxUx3JychAdHY1t27Zptcp4enpCJpNhyJAhzbLwyVYfIiIiIqIWSs8rZurk1KlTgpmZmfDpp5/WGFepVMJf//pX4fXXXxdu3rxZayvQlStXalxK/+yPvb29YGlpqXktk8kEQahuLQIg7NixQ+jSpYvonp49ewoHDhzQ5dunPzh27JgwdOhQre9d//79m/z7kJeXJ8yePVto3769Vj7m5ubC+PHjhUOHDglqtbpJ83rVqFQqYfv27cKAAQNq/D5MmjRJOHPmjL7TrBFbfYiIiIiIWr4WsWKld+/eqKysrDVuYmIiaskBALVajXv37sHY2FizisTR0RFCLZ1Ply5dwt/+9jeUlpYCACQSCf75z3/i3r17ePToEQDg008/1VzPzWmb1oULFzBv3jxs2bJFNO7s7IzFixfDy8urSVYhqFQqpKenQ6FQICMjQ+vnycnJCVKpFL6+vly9pGMlJSVITExEbGwsLl++LIrZ2dkhJCQEwcHBaN++vZ4yrB1bfYiIiIiIDEeLKKw0xI0bN2BnZ4cOHTrg9u3bz7327t27+Oijj3Dv3j0AgLu7O9avX4/x48drfZAHAA8PD6xevRo9evTQSe70fwoKChAZGQmlUilqjXB0dMTChQvx+eefN+io7YbkoVQqkZCQgPz8fFHM1NQU3t7ekEqlcHd3b5ZtJoYkPz8fK1asQHx8vKbo+UzPnj0hk8ng4+OjlyO1n4etPkREREREhqnFbF5bH2fPnsXNmzcBVK8sGThwYK3XlpSUYPDgwTh27BiA6hUQWVlZuHr1Kr744gv89ttvmmttbW0RGxvLzWmbwIMHD7BkyRIsX74c5eXlmvH27dtj3rx5CAwM1PlKIbVajb1790KhUCAtLU3rg7CjoyMCAwPh7++PDh066DQXAk6cOAG5XI6UlBSoVCpRzMPDAzKZDB9++GGzKkgIgoBjx44hMTERmzdv1trQGAAGDBgAPz8/fPbZZ9yDh4iIiIioBTLIwkpdqVQqfPLJJ0hPTwcAdO7cGXv37kVCQgI3p9WTJ0+eIC4uDt9++y0eP36sGW/bti1mzJiB0NBQtG7dWqc5FBYWYt26dYiPj0deXp4oZmxsjGHDhkEqlWLo0KFNslrmVaZWq5Geno7o6Gjs379fFDMzM8PYsWMhk8nQu3dv/SRYC7b6EBERERG9Ogy2FehFBEGAVCrVFFWsra0xa9YsDB06FNevX9dc17NnT8THxz931Qu9vMrKSqxduxaRkZG4c+eOZtzc3BxTpkzBrFmzYGtrq7PnC4KArKwsKBQKbNu2DVVVVaK4vb09AgICMGnSJDg4OOgsD6pWWlqKpKQkxMTE4MKFC6KYjY0NgoODERISAnt7ez1lqI2tPkREREREr6ZXdsVKREQEFixYAABo1aoV+vXrhwMHDmji3Jy2aajVaqSkpGDevHmi1SHGxsaYMGEC5s+fr9NCxsOHD5GcnAyFQoFz585pxYcOHQqpVIphw4bBzMxMZ3lQtdu3b2PlypVYvXo17t+/L4q9+eabCAsLg6+vLywtLfWUoRhbfYiIiIiI6JUorPz222+4dOkSLCws0L9/f2zatAmBgYGa+GuvvSbax4Ob0+qeIAjIyMjA7NmzcerUKVFs5MiRWLhwIXr27KmzZ+fk5EChUCAlJQVlZWWiuK2tLfz9/REYGIju3bvrJAcSy83NRUxMDDZu3Kh1Api7uztkMhm8vLyazSoPtvoQEREREdEzBl1YycnJQWhoKA4dOqQZs7KyQmlpaY3HLtvZ2SEmJoab0+rYoUOHMHv2bNEKIQD44IMPsHjxYri5uenkuSUlJdi0aRMUCgVOnDihFR80aBCkUim8vb1hbm6ukxzo/wiCgD179kAul+Onn34SxUxNTSGRSBAWFgZXV1c9ZSjGVh8iIiIiIqqJwRZWsrOzMXjwYJSWltbpem5Oq3tnzpzB3LlzkZaWJhp3dXXFkiVL4OHhoZPnnj59GgqFAhs2bEBxcbEoZm1tDV9fXwQFBaFXr146eT6JlZeXY+PGjZDL5VqrPaytrREUFISpU6eic+fOesrw/7DVh4iIiIiIXsQgCyuCIKBv3744efLkC6/l5rS6d/XqVcyfPx/JycmilUJOTk6IiorCyJEjG32FUFlZGbZu3QqFQoHDhw9rxd3c3CCVSiGRSJrNfh2GrrCwEKtWrcLKlStRWFgoinXr1g2hoaGYMGGCzk99qgu2+hARERERUV0Z5KlAx44dq1NRxcnJCSdPnuTmtDpy584dREVFQaFQiE7Z6dSpEyIiIuDn5wdT08b9ETx//jzi4+ORmJiotbrAysoKPj4+CAoKQt++fRv1uVS7c+fOISYmBklJSaioqBDF+vfvD5lMhk8++UTvR1ez1YeIiIiIiBrCIAsrNf2GuSZVVVUsquhAUVERli5dCrlcjidPnmjG27Vrhzlz5iAkJAQWFhaN9rzKykrs2LEDCoUCmZmZWnEXFxcEBwfDx8eHrRpNRBAE7Nu3D9HR0di9e7coZmxsjFGjRkEmk+G9997TU4bV2OpDREREREQvyyALK3XdeJRFlcZVXl6OVatWYdGiRaKjci0tLREWFobp06fj9ddfb7TnXblyBQkJCVAqlbh7964oZm5uDolEAqlUin79+nEz4iZSWVmJzZs3Qy6X4/Tp06JYmzZtEBAQgKlTp8LR0VE/Cf5/bPUhIiIiIqLGYpCFlcGDB8PMzEzUflITT0/PJsrIsKlUKiQlJSEiIgI3btzQjJuamiIoKAhfffUVOnbs2GjPSk9Ph0KhQEZGhtbpTk5OTpBKpfD19eVGxE3o/v37iI+Px4oVK3Dr1i1RrEuXLpg2bRomTpwIa2trPWXIVh8iIiIiItINg9y8FgAmTJiAxMTEWuOtWrVCbm4unJycmi4pAyMIAlJTUzF37lz8/vvvmnEjIyOMHTsWCxYsQPfu3RvlWQUFBVAqlUhISEB+fr4oZmpqCm9vb0ilUri7u3N1ShO6ePEiYmNjsW7dOpSVlYlibm5uCA8Ph7e3d6PvpVNXbPUhIiIiIiJdM9jCSklJCT7++GNkZWVpxczMzLBp0yaMGjVKD5kZhszMTMyaNQvZ2dmicS8vL0RFReGdd9556Weo1Wrs3bsXCoUCaWlpWisMHB0dERgYCH9/f3To0OGln0d1IwgCDhw4ALlcjp07d4pWDRkZGWHEiBGQyWR4//339VbkYqsPERERERE1FYMtrADVS/+Tk5OxZs0aXLx4ERYWFhg+fDimTp0KZ2dnfafXIh0/fhxz5szBjz/+KBrv378/Fi9e3CjHVhcWFmLdunWIj49HXl6eKGZsbIxhw4ZBKpVi6NChej9J5lVSVVWFrVu3Qi6X4/jx46KYlZUV/P39MW3atEZbpVRfbPUhIiIiIiJ9MOjCCjWeCxcuYN68ediyZYto3NnZGYsXL4aXl9dLrU4QBAFZWVlQKBTYtm2b1v449vb2CAgIwKRJk+Dg4NDg51D9PXr0CAkJCVi2bJlWG1anTp3w5ZdfIiAgAO3atWvy3NjqQ0RERERE+maQm9dS4ykoKEBkZCSUSqVoBYCjoyMWLlyIzz///KVWjTx8+BDJyclQKBQ4d+6cVnzo0KGQSqUYNmwYzMzMGvwcqr+8vDzExcVBqVSKjs0GgD59+iA8PByjR4/Wy/eFrT5ERERERNRcsLBCNXrw4AGWLFmC5cuXo7y8XDPevn17zJs3D4GBgQ0+rloQBOTk5EChUCAlJUVr01NbW1v4+/sjMDBQb20lrypBEHD48GHI5XKkpqZCrVaL4sOHD0d4eDgGDRrU5PunsNWHiIiIiIiaIxZWSOTJkyeIi4vDt99+i8ePH2vG27ZtixkzZiA0NBStW7du0NwlJSXYtGkTFAoFTpw4oRUfNGgQpFIpvL29YW5u3uD3QPWnUqmwfft2yOVyHD16VBSzsLCAn58fQkNDm/wULbb6EBERERFRc8fCCgEAKisrsXbtWkRGRuLOnTuacXNzc0yZMgWzZs2Cra1tg+Y+ffo0FAoFNmzYgOLiYlHM2toavr6+CAoKQq9evV7qPVD9FRUVQalUIi4uDteuXRPFOnbsiClTpiAoKKjB3/uGYqsPERERERG1FCysvOLUajVSUlIwb9480Qk8xsbGmDBhAubPn9+gzWLLysqwdetWKBQKHD58WCvu5uYGqVQKiUQCS0vLl3oPVH/Xr1/HsmXLkJCQgKKiIlHMxcUF4eHhGDNmTJOuHGKrDxERERERtUQsrLyiBEFARkYGZs+ejVOnToliI0eOxMKFC9GzZ896z3v+/HnEx8cjMTFRq23DysoKPj4+CAoKQt++fV8qf2qYnJwcREdHY9u2bVqFC09PT8hkMgwZMqTJ9k9hqw8REREREbV0LKy8gg4dOoTZs2fjwIEDovEPPvgAixcvhpubW73mq6ysxI4dO6BQKJCZmakVd3FxQXBwMHx8fPjBWA+ePn2KtLQ0yOVyHDx4UBQzNzfHuHHjEBoairfffrvJcmKrDxERERERGQoWVl4hZ86cwdy5c5GWliYad3V1xZIlS+Dh4VGv+a5cuYKEhAQolUrcvXtXFDM3N4dEIoFUKkW/fv2a/AQZqt4sODExEbGxsbh8+bIoZmdnh5CQEAQHB6N9+/ZNkg9bfYiIiIiIyBCxsPIKuHr1KubPn4/k5GQIgqAZd3JyQlRUFEaOHFnnwodKpUJ6ejoUCgUyMjJE8z2bUyqVwtfXFzY2No36Pqhu8vPzsWLFCsTHx+PRo0eiWM+ePSGTyeDj4wMLCwud58JWHyIiIiIiMnQsrBiwO3fuICoqCgqFAlVVVZrxTp06ISIiAn5+fjA1rduPQEFBAZRKJRISEpCfny+KmZqawtvbG1KpFO7u7lydoicnTpyAXC5HSkoKVCqVKObh4QGZTIYPP/ywSVaCsNWHiIiIiIheFSysGKCioiIsXboUcrkcT5480Yy3a9cOc+bMQUhISJ1WK6jVauzduxcKhQJpaWlarRuOjo4IDAyEv78/OnTo0Ojvg15MrVYjPT0d0dHR2L9/vyhmZmaGsWPHQiaToXfv3jrPha0+RERERET0KmJhxYCUl5dj1apVWLRoEe7fv68Zt7S0RFhYGKZPn47XX3/9hfMUFhZi3bp1iI+PFx3BDFQfwzxs2DBIpVIMHToUJiYmjf02qA5KS0uRlJSEmJgYXLhwQRSzsbFBcHAwQkJCYG9vr9M82OpDRERERESvOhZWDIBKpUJSUhIiIiJw48YNzbipqSmCgoLw1VdfoWPHjs+dQxAEZGVlQaFQYNu2baLWIQCwt7dHQEAAJk2aBAcHB528D3qx27dvY+XKlVi9erWoeAYAb775JsLCwuDr6wtLS0ud5sFWHyIiIiIiomosrLRggiAgNTUVc+fOxe+//64ZNzIywtixY7FgwQJ07979uXM8fPgQycnJUCgUOHfunFZ86NChkEqlGDZsGMzMzBr9PVDd5ObmIiYmBhs3bkRlZaUo5u7uDpl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   "source": [
    "circuit(xor4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "fragment"
    }
   },
   "source": [
    "Back to powerpoint"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "...."
   ]
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  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "__Q:__ Write NAND-CIRC code to compute $XOR:\\{0,1\\}^2 \\rightarrow \\{0,1\\}$ such that $XOR(a,b) = a+b \\mod 2$.\n",
    "\n",
    "Reminder AON-CIRC code is:\n",
    "```python\n",
    "t1      = AND(X[0],X[1])\n",
    "nott1   = NOT(t1)\n",
    "t2      = OR(X[0],X[1])\n",
    "Y[0]    = AND(nott1,t2)\n",
    "```"
   ]
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def parseline(line):\n",
    "    variable_name, operation = line.split('=')\n",
    "    op_name, args = operation.split('(')\n",
    "    arg1, *rest = args.strip(')').split(',')\n",
    "    arg2 = rest[0].strip() if rest else ''\n",
    "    return [variable_name.strip(), op_name.strip(), arg1.strip(), arg2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def AON2NAND(code):\n",
    "    output = \"\"; counter = 0\n",
    "    for line in code.split(\"\\n\"):\n",
    "        if not line: continue\n",
    "        foo,op,bar,blah = parseline(line) \n",
    "        # helper: parses \"foo = op(bar,blah)\"\n",
    "        if op==\"NOT\":\n",
    "            output += f\"{foo} = NAND({bar},{bar})\\n\"\n",
    "        if op==\"AND\": \n",
    "            output += f\"temp_{counter} = NAND({bar},{blah})\\n\"\n",
    "            output += f\"{foo} = NAND(temp_{counter},temp_{counter})\\n\"\n",
    "            counter +=1\n",
    "        if op==\"OR\":\n",
    "            output += f\"temp_{counter} = NAND({bar},{bar})\\n\"\n",
    "            output += f\"temp_{counter+1} = NAND({blah},{blah})\\n\"\n",
    "            output += f\"{foo} = NAND(temp_{counter},temp_{counter+1})\\n\"\n",
    "            counter +=2\n",
    "    return output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "temp_0 = NAND(X[0],X[1])\n",
      "t1 = NAND(temp_0,temp_0)\n",
      "nott1 = NAND(t1,t1)\n",
      "temp_1 = NAND(X[0],X[0])\n",
      "temp_2 = NAND(X[1],X[1])\n",
      "t2 = NAND(temp_1,temp_2)\n",
      "temp_3 = NAND(nott1,t2)\n",
      "Y[0] = NAND(temp_3,temp_3)\n",
      "\n"
     ]
    },
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   "source": [
    "xornand = AON2NAND(xorcode)\n",
    "print(xornand)\n",
    "circuit(FUNC(xornand))"
   ]
  },
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    "slideshow": {
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   "source": [
    "# Q: what does this program compute?\n",
    "mystery='''\n",
    "u = NAND(X[0],X[1])\n",
    "v = NAND(X[0],u)\n",
    "w = NAND(X[1],u) \n",
    "Y[0] = NAND(v,w)'''"
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   "outputs": [],
   "source": [
    "m = FUNC(mystery)\n",
    "circuit(m)"
   ]
  },
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   "metadata": {
    "slideshow": {
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   "source": [
    "table(m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "__Q:__ Design a NAND circuit to compute $XOR4:\\{0,1\\}^4 \\rightarrow \\{0,1\\}$ where $XOR4(a,b,c,d) = a+b+c+d \\mod 2$"
   ]
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   "source": [
    "def XOR2(a,b):\n",
    "    u = NAND(a,b)\n",
    "    v = NAND(a,u)\n",
    "    w = NAND(b,u)\n",
    "    return NAND(v,w)\n",
    "\n",
    "def XOR4(a,b,c,d):\n",
    "    u = XOR2(a,b)\n",
    "    v = XOR2(c,d)\n",
    "    return XOR2(u,v)\n",
    "\n",
    "XOR4circ = circuit(XOR4)"
   ]
  },
  {
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   "execution_count": null,
   "metadata": {
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   "outputs": [],
   "source": [
    "table(XOR4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
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   },
   "outputs": [],
   "source": [
    "print(AON(XOR4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
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   "source": [
    "## Next Up:\n",
    "\n",
    "__Theorem:__ For _every_ function $f:\\{0,1\\}^n \\rightarrow \\{0,1\\}^m$ there exists a Boolean circuit to compute $f$.\n",
    "\n",
    "__Corollary:__ For every such $f$, there is AON-CIRC program/NAND circuit/NAND-CIRC program to compute $f$."
   ]
  }
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